稀疏矩阵的存储及运算

稀疏矩阵的存储及运算存储什么是稀疏矩阵？人们无法给出确切的定义，它只是一个凭人们的直觉来了解的概念。

假若在m*n的矩阵中，非零元个数num<<m+n，我们可以称之为稀疏矩阵，并称t= num/(m*n) 为矩阵的稀疏因子。

通常认为t<<0.05时称为稀疏矩阵。

存储稀疏矩阵时，往往只存放其中的非零元。

稀疏矩阵的三元组表法是顺序存储方法的一种。

采用这种方法时，线性表中的每个结点对应稀疏矩阵的一个非零元素，其中包括3个字段，分别为该元素的行下标、列下标和值，结点间的次序按矩阵的行优先顺序排列。

另外，用第0行的三个元素分别存储矩阵的行数、列数和非零元数目。

例如，矩阵A：50 0 70 1 0 010 0 0 可以用三元组表示为： 3 4 41 1 51 4 72 2 13 1 1在具体编程过程中，往往可以用一个简单的n*3二数组来表示此三元组。

即稀疏矩阵A可以用数组a[5][3]={{3,4,4},{1,1,5},{1,4,7},{2,2,1},{3,1,1}} 来表示。

运算1）矩阵转置（带回溯）由于稀疏矩阵中的元素的存储是按行优先存储的，因此三元组中数据的行下标递增有序，行下标相同时列下标递增有序。

存储转置后的矩阵，只要将三元组a的第一行依次将a中的列值由小到大进行选择，将选中的三元组元素行列值互换后放入三元组b，直到三元组a中的元素全部放入b中为止。

2）不带回溯的转置不带回溯的转置要解决的关键问题是要预先确定好矩阵的每一列第一个非零元素在三元组b中应有的位置。

为了确定这些位置，转置前必须求得三元组a 中每一列非零元的个数，从而得到每列第一个元素在三元组b中（行）的位置。

用pot数组来记录。

pot[1]=1；pot[col]=pot[col-1]+第col-1列非零元的个数（pot[col]）3）矩阵相加 C = A + B稀疏矩阵相加采用的算法思想是：依次扫描 A和B的行号和列号，如果A 的当前项的行号等于B的当前项的行号，则比较其列号，将较小的项存入C。

若列号也相等，则将对应的元素相加后存入C；若A的当前项的行号小于B的，则将A的项存入C，否则将B的项存入C。

[注]：if a[i][0]= = b[i][0]&& a[i][1]< b[i][1] 表明该位置上B矩阵为零而A矩阵的元素不为零，相加后的C矩阵的该位置元素应为A矩阵的该元素，故将较小者存入C。

4）矩阵相乘C = A * B矩阵的乘法涉及到两矩阵不同行，列之间的运算，情况相对复杂。

稀疏矩阵的乘法采用普通矩阵相乘的基本方法，关键是通过给顶的行号和列号找出原矩阵对应的元素值。

这里设计一个函数value，当在三元组表示中找到时返回其元素值，找不到时，说明该位置为0，因此返回0。

然后利用该函数计算出C的行号i和列号j 处的元素值，若该值不为0，则存入其三元组表示的矩阵，否则不存入。

完整的参考C程序如下:#include <stdio.h>#define max 20convert(int a[max][3],int a1[max][3]){int p,q,col;a1[0][0]=a[0][1];a1[0][1]=a[0][0];a1[0][2]=a[0][2];if(a1[0][2]!=0){q=1;for(col=1;col<=a[0][1];col++)for(p=1;p<=a[0][2];p++)if(a[p][1]==col){a1[q][1]=a[p][0];a1[q][0]=a[p][1];a1[q][2]=a[p][2];q++;}}}add(int a[max][3],int b[max][3],int c[max][3]) //error!!{int i=1,j=1,k=1;while(i<=a[0][2]&&j<=b[0][2]){if(a[i][0]==b[j][0]){if(a[i][1]<b[j][1]){c[k][0]=a[i][0];c[k][1]=a[i][1];c[k][2]=a[i][2];k++;i++;}else if(a[i][1]>b[j][1]) {c[k][0]=b[j][0];c[k][1]=b[j][1];c[k][2]=b[j][2];k++;j++;}else{c[k][0]=b[j][0];c[k][1]=b[j][1];c[k][2]=a[i][2]+b[j][2]; k++;i++;j++;}}else if(a[i][0]<b[j][0]) {c[k][0]=a[i][0];c[k][1]=a[i][1];c[k][2]=a[i][2];k++;i++;}else{c[k][0]=b[j][0];c[k][1]=b[j][1];c[k][2]=b[j][2];k++;j++;}c[0][0]=a[0][0];c[0][1]=a[0][1];c[0][2]=k-1;}}int value(int c[max][3],int i,int j){int k=1;while(k<=c[0][2]&&!(c[k][0]==i&&c[k][1]==j)) k++;if(c[k][0]==i&&c[k][1]==j)return(c[k][2]);else return(0);}multi(int a[max][3],int b[max][3],int c[max][3]) {int i,j,p,s,q;p=1;for(i=1;i<=a[0][0];i++)for(j=1;j<=b[0][1];j++){s=0;for(q=1;q<=a[0][1];q++)s=s+value(a,i,q)*value(b,q,j);if(s!=0){c[p][0]=i;c[p][1]=j;c[p][2]=s;p++;}}c[0][0]=a[0][0];c[0][1]=b[0][1];c[0][2]=p-1;}print(int a[max][3]){int i,j;for(i=0;i<=a[0][2];i++){for(j=0;j<=2;j++)printf(" %d",a[i][j]);printf("/n");}}main(){int a[max][3],b[max][3],a1[max][3],b1[max][3],c[max][3],d[max][3]; int i,y;printf("输入稀疏方阵A的行数，列数和非零元个数：");scanf("%d,%d,%d",&a[0][0],&a[0][1],&a[0][2]);for(i=1;i<=a[0][2];i++){printf("输入第%d个非0元素的行数，列数和值:",i);scanf("%d,%d,%d",&a[i][0],&a[i][1],&a[i][2]);}printf("输出A的三元组表示：/n");print(a);printf("/n输入稀疏方阵B的行数，列数和非零元个数：");scanf("%d,%d,%d",&b[0][0],&b[0][1],&b[0][2]);for(i=1;i<=b[0][2];i++){printf("输入第%d个非0元素的行数，列数和值:",i);scanf("%d,%d,%d",&b[i][0],&b[i][1],&b[i][2]);}printf("输出B的三元组表示：/n");print(b);printf("/n");printf("============= 菜单==============/n");printf(" 1 A矩阵转置/n");printf(" 2 B矩阵转置/n");printf(" 3 C = A + B/n");printf(" 4 D = A * B/n");printf("======================================/n/n");loop: printf("请选择相应操作的序号:");scanf("%d",&y);switch(y){case 1: convert(a,a1);printf("输出A转置的三元组表示：/n");print(a1);printf("/n");goto loop;case 2: convert(b,b1);printf("输出B转置的三元组表示：/n");print(b1);printf("/n");goto loop;case 3: add(a,b,c);printf("输出C=A+B的三元组表示：/n");print(c);printf("/n");goto loop;case 4: multi(a,b,d);printf("输出D=A*B的三元组表示：/n");print(d);printf("/n");goto loop;}}哪个提问。

记不住了。

补充：#include<iostream>using namespace std;class Matrix{private:int row,col;double **mx;public:Matrix(){}~Matrix();Matrix(Matrix &m);Matrix(int n,int m);friend Matrix operator*(Matrix &,Matrix &);friend istream & operator >>(istream &,Matrix &); friend ostream & operator <<(ostream &,Matrix &); friend Matrix operator+(Matrix &,Matrix &);friend Matrix operator-(Matrix &,Matrix &);friend Matrix operator!(Matrix &);};Matrix::Matrix(Matrix &m){int i,j;row=m.row;col=m.col;mx=new double *[row];for(i=0;i<row;i++)mx[i]=new double[col];for(i=0;i<m.row;i++)for(j=0;j<m.col;j++)mx[i][j]=m.mx[i][j];}Matrix::~Matrix(){int i;for(i=0;i<row;i++)delete [] mx[i];delete []mx;}Matrix::Matrix(int n,int m){int i,j;row=n;col=m;mx=new double *[row];for(i=0;i<row;i++)mx[i]=new double[col];for(i=0;i<row;i++)for(j=0;j<col;j++)mx[i][j]=0;}istream& operator>>(istream &input,Matrix &m) {int i,j;for(i=0;i<m.row;i++)for(j=0;j<m.col;j++)input>>m.mx[i][j];return input;}Matrix operator+(Matrix &m1,Matrix &m2){Matrix m(m1.row,m1.col);int i,j;for(i=0;i<m1.row;i++)for(j=0;j<m1.col;j++)m.mx[i][j]=m1.mx[i][j]+m2.mx[i][j];return m;}Matrix operator*(Matrix &m1,Matrix &m2){if(m1.col!=m2.row)throw 1;Matrix m(m1.row,m2.col);int i,j,t=0,s,l=0;for(i=0;i<m.col*m.row;i++){for(j=0,s=0;j<m2.row,s<m1.col;j++,s++) {m.mx[t][l]+=m1.mx[t][j]*m2.mx[s][l];}if((i+1)%m.col==0) {t++;l=0;}else l++;}return m;}ostream& operator<<(ostream &output,Matrix &m) {int i,j;for(i=0;i<m.row;i++)for(j=0;j<m.col;j++){output<<m.mx[i][j]<<"\t";if(j==m.col-1) cout<<endl;}return output;}Matrix operator-(Matrix &m1,Matrix &m2){Matrix m(m1.row,m1.col);int i,j;for(i=0;i<m1.row;i++)for(j=0;j<m1.col;j++)m.mx[i][j]=m1.mx[i][j]-m2.mx[i][j];return m;}Matrix operator!(Matrix &m1){int i,j;Matrix m(m1.col,m1.row);for(i=0;i<m1.row;i++)for(j=0;j<m1.col;j++)m.mx[j][i]=m1.mx[i][j];return m;}int main(){int n,m;int n1,n2;cout<<"**********加法与减法**********"<<endl; cout<<"请输入行数与列数：";cin>>n>>m;Matrix m1(n,m);cout<<"输入第一个矩阵："<<endl;cin>>m1;Matrix m2(n,m);cout<<"输入第二个矩阵："<<endl;cin>>m2;Matrix m3(m1+m2);cout<<"两矩阵相加后："<<endl;cout<<m3<<endl;cout<<"两矩阵相减后："<<endl;Matrix m31(m1-m2);cout<<m31<<endl;cout<<"**********乘法*********"<<endl;cout<<"请输入第一个矩阵的行与列：";cin>>n>>m;Matrix m4(n,m);cout<<"输入第一个矩阵："<<endl;cin>>m4;cout<<"请输入第二个矩阵的行与列：";cin>>n1>>n2;Matrix m5(n1,n2);cout<<"输入第二个矩阵："<<endl;cin>>m5;try{Matrix m6(m4*m5);cout<<"两矩阵相乘后："<<endl;cout<<m6<<endl;}catch(int){cout<<"第一个矩阵的列数不等于第二个矩阵的行数，所以不能相乘！"<<endl;}cout<<"**********转置**********"<<endl;cout<<"请输入矩阵的行与列：";cin>>n>>m;Matrix m7(n,m);cout<<"输入一个矩阵："<<endl;cin>>m7;Matrix m8(!m7);cout<<"转置后："<<endl;cout<<m8;return 0;}-----------------------------------------------------------------------S P A R S K I T V E R S I O N 2.-----------------------------------------------------------------------Latest update : Tue Mar 8 11:01:12 CST 2005-----------------------------------------------------------------------Welcome to SPARSKIT VERSION 2. SPARSKIT is a package of FORTRAN subroutines for working with sparse matrices. It includes general sparse matrix manipulation routines as well as a fewiterativesolvers, see detailed description of contents below.Copyright (C) 2005, the Regents of the University of MinnesotaSPARSKIT is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation [version 2.1 of the License, or any later version.]A copy of the licencing agreement is attached in the file LGPL. For additional information contact the Free Software Foundation Inc., 59 Temple Place - Suite 330, Boston, MA 02111, USA or visit the web-site/copyleft/lesser.htmlDISCLAIMER----------SPARSKIT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warrantyofMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.For more information contact saad@---------------------------------------------------S P A R S K I T VERSION 2---------------------------------------------------In this directory you will find all relevant subdirectories and the Unix makefile which will compile all the modules and make a unix library libskit.a. Please read the makefile. Making the library should be the first thing to do when starting to use the package. Some of the objects will be linked into a librarycalledlibskit.a. Others will not be linked but can be used by other makefiles for test problems provided in the subdirectories. You can then link to libskit.a by default instead of theindividualmodules. (Please report any compilation problems or (even minor) warnings immediatly to saad@). Once this is done, it is recommended to run the test problems provided. There are various test suites in each of the subdirectories and makefiles are available for each. See explanations in the README files in each individual subdirectory.You may also make and run the test programs using the dotests script provided in this directory. Output from this script may be redirected into a file and compared to the sample output files out.xxx. There is an additional script called sgrep which is useful for looking for tools in all the subdirectories. Read the sgrep fileforinstructions.-----------------------------------------------------------------------Here is some information on the SPARSKIT sub-directories.BLASSM : Basic linear algebra with sparse matrices.contains two modules: blassm.f and matvec.fDOC : contains the main documentation of the packageINFO : information routine (new one) . Info2 (spectralinformation) not available yet.FORMATS: Contains the Format Conversion routines informats.f and the manipulation routines inunary.fINOUT : input output routines. contains the module inout.fITSOL : contains the iterative solution package. Variousiterative solvers and preconditioners are provided.MATGEN : matrix generation routines.contains the module genmat.f and several subroutinescalled by it. Also contains zlatev.f (contributedby E. Rothman, from Cornell).ORDERINGS:still in the works. But contains a few coloring routinesand level-set related orderings -- (e.g., cuthill Mc Kee, etc.)UNSUPP : various `unsupported' routines and drivers.(misc. routines includind routines forplotting.. BLAS1 is also added for completeness)See the file "logfile" for a complete revision history.Report any problems, suggestions, etc.. toYousef Saad.saad at cs dot umn dot edu-----------------------------------------------------------------------稀疏矩阵运算器（纯C编写#include "string.h"#include "ctype.h"#include "malloc.h"#include "stdio.h"#include "stdlib.h"#include "conio.h"#include "mem.h"#include "alloc.h"#define OK 1#define ERROR 0#define MAXSIZE 100#define MAXRC 20typedef int Status;typedef int ElemType;typedef struct{int i,j;ElemType e;}Triple;typedef struct{Triple data[MAXSIZE+1]; /* 非零元三元组表,data[0]未用 */ int rpos[MAXRC+1]; /* 各行第一个非零元素的位置表*/int mu,nu,tu; /* 矩阵的行数、列数和非零元个数*/}RLSMatrix;typedef struct OLNode{int i,j;ElemType e;struct OLNode *right,*down;}OLNode,*OLink;typedef struct{OLink *rhead,*chead;int mu,nu,tu;}CrossList;Status CreateSMatrix(RLSMatrix *M);void DestroySMatrix(RLSMatrix *M);void PrintSMatrix(RLSMatrix M);Status ADD(RLSMatrix M,RLSMatrix N,RLSMatrix *Q);Status SubtS(RLSMatrix M,RLSMatrix N,RLSMatrix *Q);Status Mult(RLSMatrix M,RLSMatrix N,RLSMatrix *Q);Status FastTransposeSMatrix(RLSMatrix M,RLSMatrix *T);int menu_select();Status Operate(RLSMatrix A,RLSMatrix B,RLSMatrix *C);Status Exchange(RLSMatrix M,CrossList *N);Status Show(CrossList N);Status Change(RLSMatrix A,RLSMatrix B,RLSMatrix C,CrossList *M);Status DestoryCrossList(CrossList *M);void About();main(){RLSMatrix A,B,C;CrossList N;clrscr();About();for(;;){switch(menu_select()) /*调用主菜单函数，返回值做开关语句的条件*/{case 1:clrscr();printf("\n\n\n\t-------------Create Sparse Matrix A-----------------"); CreateSMatrix(&A); break;case 2:clrscr();printf("\n\n\n\t-------------Create Sparse Matrix B-----------------"); CreateSMatrix(&B); break;case 3:Operate(A,B,&C);break;case 4:Change(A,B,C,&N); break;case 5:About();break;case 6:DestroySMatrix(&A);DestroySMatrix(&B);DestroySMatrix(&C);DestoryCrossList(&N);exit(0);}}}int menu_select(){char *menu[]={"","",""," +--------------MENU--------------+", /*定义菜单字符串数组*/ " | |"," | 1.Create Sparse Matrix A |"," | 2.Create Sparse Matrix B |"," | 3.Operate |"," | 4.Change into CrossList |"," | 5.About... |"," | 6.Quit |"," | |"," | |"," +--------------------------------+"," By Zacard"," 06 07 10",};char s[3]; /*以字符形式保存选择号*/int c,i; /*定义整形变量*/gotoxy(1,25);printf("Any key to enter menu......\n");getch();clrscr();for(i=0;i<16;i++) /*输出主菜单数组*/{ gotoxy(10,i+1);cprintf("%s",menu[i]);}window(1,1,80,25); /*恢复原窗口大小*/gotoxy(10,21);do{printf("\n Enter your choice(1~6):");scanf("%s",s);c=atoi(s); /*将输入的字符串转化为整形数*/}while(c<1||c>6);return c; /*返回选择项，主程序根据该数调用相应的函数*/}Status CreateSMatrix(RLSMatrix *M) /* 创建稀疏矩阵M */{int i; /*用于暂存data域内容*/Triple T;int flag=0,mis; /*标志，输入正确为0*/printf("\nPlease input the row,col,and nonzero element number of the Sparse Matrix.");printf("\nForm:row num,col num,nonzero element num\n");scanf("%d,%d,%d",&(*M).mu,&(*M).nu,&(*M).tu);(*M).data[0].i=0; /* 为以下比较做准备 */for(i=1;i<=(*M).tu;i++){ mis=0;do{if(flag){printf("ERROR INPUT!\n");flag=0;mis++;}if(mis==3){printf("Fail Create !");return OK;}printf("Please input the row,col and value of the %dth nonzero element:",i);scanf("%d,%d,%d",&T.i,&T.j,&T.e);if(T.i<1||T.i>(*M).mu||T.j<1||T.j>(*M).nu) /* 行或列超出范围 */flag=1;if(T.i<(*M).data[i-1].i||T.i==(*M).data[i-1].i&&T.j<=(*M).data[i-1].j) /* 没有按顺序输入非零元素 */ flag=1;}while(flag); /* 当输入有误,重新输入 */(*M).data[i]=T;}for(i=1;i<=(*M).tu;i++) /* 计算rpos[] */for(T.i=0;T.i<(*M).data[i].i-(*M).data[i-1].i;T.i++) /* (*M).data[i]为第一个非0元素 */(*M).rpos[(*M).data[i].i-T.i]=i;for(i=(*M).data[(*M).tu].i+1;i<=(*M).mu;i++) /* 给最后没有非零元素的几行赋值 */(*M).rpos[i]=(*M).tu+1;PrintSMatrix(*M);return OK;}void PrintSMatrix(RLSMatrix M) /* 输出稀疏矩阵M */{int i,j,k;printf("\n ");for(i=1,k=1;i<=M.mu;i++){for(j=1;j<=M.nu;j++){if(M.data[k].i==i&&M.data[k].j==j){printf("%d\t",M.data[k].e); k++;}else printf("0\t");while(j==M.nu){printf("\n ");break;}}}}Status ADD(RLSMatrix M,RLSMatrix N,RLSMatrix *Q) /* 求稀疏矩阵的和Q=M+N */{int k,p,q;if(M.mu!=N.mu||M.nu!=N.nu) return ERROR;(*Q).mu=M.mu;(*Q).nu=M.nu;(*Q).tu=0;M.rpos[M.mu+1]=M.tu+1; /* 为方便后面的while循环临时设置 */N.rpos[N.mu+1]=N.tu+1;for(k=1;k<=M.mu;++k) /* 对于每一行，k指示行号 */{(*Q).rpos[k]=(*Q).tu+1;p=M.rpos[k]; /* p指示M矩阵第k行当前元素的序号 */q=N.rpos[k]; /* q指示N矩阵第k行当前元素的序号 *//* 当某一行不存在非零元素时，它对应的非零位置表的值为下一个非零元素的位置*/while(p<M.rpos[k+1]&&q<N.rpos[k+1]) /* 故当某行非零元位置等于下一行非零元位置时，它不存在非零元素*/ { /* M,N矩阵均有第k行元素未处理 */if(M.data[p].j==N.data[q].j) /* M矩阵当前元素和N矩阵当前元素的列相同 */{(*Q).data[(*Q).tu+1].e=M.data[p].e+N.data[q].e; /* 位置相同*/if((*Q).data[(*Q).tu+1].e!=0) /* 相加结果为0?*/{++(*Q).tu;(*Q).data[(*Q).tu].i=k;(*Q).data[(*Q).tu].j=M.data[p].j;}++p;++q;}else if(M.data[p].j<N.data[q].j){ /* M矩阵当前元素的列<N矩阵当前元素的列 */++(*Q).tu;(*Q).data[(*Q).tu].e=M.data[p].e;(*Q).data[(*Q).tu].i=k;(*Q).data[(*Q).tu].j=M.data[p].j;++p;}else /* M矩阵当前元素的列>N矩阵当前元素的列 */{++(*Q).tu;(*Q).data[(*Q).tu].e=N.data[q].e;(*Q).data[(*Q).tu].i=k;(*Q).data[(*Q).tu].j=N.data[q].j;++q;}}while(p<M.rpos[k+1]) /* M矩阵还有k行的元素未处理 */{++(*Q).tu;(*Q).data[(*Q).tu].e=M.data[p].e;(*Q).data[(*Q).tu].i=k;(*Q).data[(*Q).tu].j=M.data[p].j;++p;}while(q<N.rpos[k+1]) /* N矩阵还有k行的元素未处理 */{++(*Q).tu;(*Q).data[(*Q).tu].e=N.data[q].e;(*Q).data[(*Q).tu].i=k;(*Q).data[(*Q).tu].j=N.data[q].j;++q;}}return OK;}Status SubtS(RLSMatrix M,RLSMatrix N,RLSMatrix *Q) /* 求稀疏矩阵的差Q=M-N */ {int i;if(M.mu!=N.mu||M.nu!=N.nu) return ERROR;for(i=1;i<=N.tu;++i) /* 对于N的每一元素,其值乘以-1 */N.data[i].e*=-1;ADD(M,N,Q); /* Q=M+(-N) */return OK;}Status Mult(RLSMatrix M,RLSMatrix N,RLSMatrix *Q) /* 求稀疏矩阵乘积Q=M＊N*/ {int arow,brow,p,q,ccol,ctemp[MAXRC+1]; /* ctemp[MAXRC+1]为列元素累加器*/if(M.nu!=N.mu) return ERROR; /* 矩阵M的列数应和矩阵N的行数相等 */(*Q).mu=M.mu; /* Q初始化 */(*Q).nu=N.nu;(*Q).tu=0;M.rpos[M.mu+1]=M.tu+1; /* 为方便后面的while循环临时设置 */N.rpos[N.mu+1]=N.tu+1;if(M.tu*N.tu!=0) /* M和N都是非零矩阵 */{for(arow=1;arow<=M.mu;++arow){ /* 从M的第一行开始，到最后一行，arow是M的当前行 */for(ccol=1;ccol<=(*Q).nu;++ccol)ctemp[ccol]=0; /* Q的当前行的各列元素累加器清零 */(*Q).rpos[arow]=(*Q).tu+1; /* Q当前行的第1个元素位于上1行最后1个元素之后 */ for(p=M.rpos[arow];p<M.rpos[arow+1];++p){ /* 对M当前行中每一个非零元 */brow=M.data[p].j; /* 找到对应元在N中的行号(M当前元的列号) */for(q=N.rpos[brow];q<N.rpos[brow+1];++q){ccol=N.data[q].j; /* 乘积元素在Q中列号 */ctemp[ccol]+=M.data[p].e*N.data[q].e;}} /* 求得Q中第arow行的非零元 */for(ccol=1;ccol<=(*Q).nu;++ccol) /* 压缩存储该行非零元 */if(ctemp[ccol]){if(++(*Q).tu>MAXSIZE) return ERROR;(*Q).data[(*Q).tu].i=arow;(*Q).data[(*Q).tu].j=ccol;(*Q).data[(*Q).tu].e=ctemp[ccol];}}}return OK;}Status FastTransposeSMatrix(RLSMatrix M,RLSMatrix *T){int col,p,q,t,num[MAXRC+1],cpot[MAXRC+1];(*T).mu=M.nu; /* num[]存M每列非0元个数 */(*T).nu=M.mu; /* cpot[]存每列第一个非0元序号 */(*T).tu=M.tu;if((*T).tu){for(col=1;col<=M.nu;++col) num[col]=0;for(t=1;t<=M.tu;++t) ++num[M.data[t].j];cpot[1]=1;for(col=2;col<=M.nu;++col) cpot[col]=cpot[col-1]+num[col-1];for(p=1;p<=M.tu;++p){col=M.data[p].j; q=cpot[col];(*T).data[q].i=M.data[p].j;(*T).data[q].j=M.data[p].i;(*T).data[q].e=M.data[p].e;++cpot[col];}}PrintSMatrix(M);printf("\nTranspose:\n");PrintSMatrix(*T);return OK;}Status Operate(RLSMatrix A,RLSMatrix B,RLSMatrix *C){int c;char t;do{clrscr();printf("\nInput your choice:\n(ADD--1,SUB--2,MUL--3,Transpose A--4,Transpose B--5,QUIT--any except 1~5)\n");scanf("%d",&c);switch(c){case 1:if(A.mu!=B.mu||A.nu!=B.nu){printf("Can't,condition misfit!\n");break;}ADD(A,B,C);PrintSMatrix(A);printf("\n\t(+)\n");PrintSMatrix(B);printf("\n\t(=)\n");PrintSMatrix(*C);break;case 2:if(A.mu!=B.mu||A.nu!=B.nu){printf("Can't,condition misfit!\n");break;}SubtS(A,B,C);PrintSMatrix(A);printf("\n\t(-)\n");PrintSMatrix(B);printf("\n\t(=)\n");PrintSMatrix(*C);break;case 3:if(A.nu!=B.mu){printf("Can't,condition misfit\n");break;}Mult(A,B,C);PrintSMatrix(A);printf("\n\t(*)\n");PrintSMatrix(B);printf("\n\t(=)\n");PrintSMatrix(*C);break;case 4:FastTransposeSMatrix(A,C);break;case 5:FastTransposeSMatrix(B,C);break;default: return OK;}/* switch */printf("Want to continue? (y/n)?");t=getch();}while(t=='y');return OK;}void DestroySMatrix(RLSMatrix *M) /* 销毁稀疏矩阵M(使M为0行0列0个非零元素的矩阵) */ {(*M).mu=0;(*M).nu=0;(*M).tu=0;}稀疏矩阵的加减法、乘法、求逆运算2010-11-16 21:27:07| 分类：数据结构与算法|举报|字号订阅#include <iostream>#include <iomanip>using namespace std;const int MAXSIZE = 100; //定义非零元素的最多个数const int MAXROW = 10; //定义数组行数的最大值const int SIZENUM = 10;typedef struct //定义三元组元素{int r, c; //矩阵的行号和列号int v; //矩阵元素值}Triple;typedef struct //定义普通三元组对象{Triple data[MAXSIZE+1];int rows, cols, nzeroNums; //行数、列数、非零元素个数}TSMatrix;typedef struct //定义行逻辑链接的顺序表{Triple data[MAXSIZE+2]; //非0元三元组表int rpos[MAXROW+1]; //各行第一个非零元素的位置表 int rows, cols, nzeroNums; //行数、列数、非零元素个数}RLSMatrix;//输入三元组矩阵template <class T>bool InputTSMatrix(T &M, int y){cout << "输入矩阵的行数、列数和非零元素个数: ";cin >> M.rows >> M.cols >> eroNums;cout << "请输入非零元素对应的行号、列号和相应的元素值: " << endl; for (int i = 1; i <= eroNums; i++){cin >> M.data[i].r >> M.data[i].c >> M.data[i].v;}return true;}//输出矩阵，按标准格式输出template <class T>bool OutputSMatrix(T M){int i, j, k = 1;for (i = 0; i < M.rows; i++){for (j = 0; j < M.cols; j++){if ((M.data[k].r-1) == i && (M.data[k].c-1) == j){cout << setw(4) << M.data[k].v;k++;}elsecout << setw(4) << "0";}//end_jcout << endl;}//end_ireturn true;}//求稀疏矩阵的转置int TranSMatrix(){TSMatrix M, T;InputTSMatrix(M, 0);int col, p, q = 1;T.rows = M.cols;T.cols = M.rows;eroNums = eroNums;if (eroNums){for (col = 1; col <= M.cols; col++){for (p = 1; p <= eroNums; p++){if (M.data[p].c == col){T.data[q].r = M.data[p].c;T.data[q].c = M.data[p].r;T.data[q].v = M.data[p].v;++q;}}//end_p}//end_col}//end_ifcout << "运用普通转置算法, 输入矩阵的转置矩阵为: " << endl;OutputSMatrix(T);return 1;}//稀疏矩阵的快速转置int FastTranMat(){TSMatrix M, T;int num[MAXROW+1]; //表示矩阵M中第col列非零元素的个数int cpot[MAXROW+1]; //表示矩阵M中第col列第一个非0元素在b.data中的位置int p, q, col, t;InputTSMatrix(M, 0); //输入稀疏矩阵T.rows = M.cols;T.cols = M.rows;eroNums = eroNums;if (eroNums){for (col = 1; col <= M.cols; col++)//M中各列元素初始化{num[col] = 0;}for (t = 1; t <= eroNums; t++){++num[M.data[t].c]; //求M中每一列非零元个数 }//求第col列第一个非零元在b.data中的序号cpot[1] = 1;for (col = 2; col <= M.cols; col++){cpot[col] = cpot[col-1] + num[col-1];}for (p = 1; p <= eroNums; p++){col = M.data[p].c; //稀疏矩阵M中每个元素对应的列号q = cpot[col]; //稀疏矩阵M中第一个非零元素位置T.data[q].r = M.data[p].c;T.data[q].c = M.data[p].r;T.data[q].v = M.data[p].v;++cpot[col];}//end_for}//end_ifcout << "运用快速算法，输入矩阵的转置为: " << endl;OutputSMatrix(T);return 1;}//求取稀疏矩阵每一行非零元个数bool Count(RLSMatrix &M){int row, p;int num[MAXROW+1];for (row = 1; row <= M.rows; row++){num[row] = 0; //清零}for (p = 1; p <= eroNums; p++){++num[M.data[p].r]; //统计M每一行非零元个数}M.rpos[1] = 1;//M中每一行非零元的起始位置for (row = 2; row <= M.rows; row++){M.rpos[row] = M.rpos[row-1] + num[row-1];}return true;}//两个稀疏矩阵的乘法bool MultSMatrix(){RLSMatrix M, N, Q; //构建三个带链接信息的三元组表示的数组 InputTSMatrix(M, 1); //用普通三元组形式输入数组InputTSMatrix(N, 1);Count(M);Count(N);if (M.cols != N.rows){cout << "Error!";return false;}//Q的初始化Q.rows = M.rows;Q.cols = N.cols;eroNums = 0;int mrow, nrow, p, q, t, tp, qcol;int ctemp[MAXROW+1]; //辅助数组//如果Q是非零矩阵if (eroNums * eroNums){for (mrow = 1; mrow <= M.rows; mrow++){//当前行各元素累加器清零for (int x = 1; x <= N.cols; x++){ctemp[x] = 0;}//end_x//当前行的首个非零元素在三元组中的位置为此行前所有非0元素加1Q.rpos[mrow] = eroNums + 1;if (mrow < M.rows){tp = M.rpos[mrow+1];}elsetp = eroNums + 1;for (p = M.rpos[mrow]; p < tp; p++) //对当前行的每个非零元素操作{nrow = M.data[p].c; //在N中找到与M操作元素的c值相等的行值rif (nrow < N.rows){t = N.rpos[nrow+1];}elset = eroNums + 1;//对找出的行的每个非零元素进行操作for (q = N.rpos[nrow]; q < t; q++){qcol = N.data[q].c;//将乘得到的对应值放在相应元素的累加器里面ctemp[qcol] += M.data[p].v * N.data[q].v;}}//p_end_for//对已经求出的累加器中的值压缩到Q中for (qcol = 1; qcol <= Q.cols; qcol++){if (ctemp[qcol]){if (++eroNums > MAXSIZE){cout << "Error!" << endl;return 0;}Q.data[eroNums].r = mrow;Q.data[eroNums].c = qcol;Q.data[eroNums].v = ctemp[qcol];}}//qcol_end_for}//arow_end_for}//end_ifcout << "两个稀疏矩阵相乘的结果为:\n";OutputSMatrix(Q);return 1;}//两个稀疏矩阵的加法int AddMatrix(){TSMatrix A, B, C;int i = 1, j = 1, k = 1; //i, j, k分别用以保存A、B、C非零元素个数 int value = 0;InputTSMatrix(A, 0);InputTSMatrix(B, 0);if (A.rows != B.rows || A.cols != B.cols){cout << "两个稀疏矩阵的大小不等,不能相加!" << endl;return 0;}if (A.rows == B.rows && A.cols == B.cols){while (i <= eroNums && j <= eroNums) {if (A.data[i].r == B.data[j].r){if (A.data[i].c < B.data[j].c){C.data[k].r = A.data[i].r;C.data[k].c = A.data[i].c;C.data[k].v = A.data[i].v;k++;i++;}else if (A.data[i].c > B.data[j].c){C.data[k].r = B.data[j].r;C.data[k].c = B.data[j].c;C.data[k].v = B.data[j].v;k++;j++;}else{value = A.data[i].v + B.data[j].v;if (value != 0){C.data[k].r = A.data[i].r;C.data[k].c = A.data[i].c;C.data[k].v = value;k++;}i++;j++;}}//end_ifelse if (A.data[i].r < B.data[j].r)。