c++ - 重载矩阵乘法 "* "运算符有问题

Question

我想为我冗长的问题道歉，这只是我第二次使用这个网站。在不久的将来，我会确保我的问题得到有序的综合。

我正在编写一个 n x m 矩阵类，其中包括重载乘法。目前，仅当第一个输入矩阵的列与第二个矩阵的行匹配时，代码才适用于 n x n 和 n x m 矩阵乘法，而不是相反。例如:

a1 a2 * b1
        b2

这会起作用(抱歉，我没有足够的声誉点来发布图像，但可以将其视为 1x2 矩阵 * 2x1 矩阵)。

a1 * b1 b2
a2

但是这种类型的输入不起作用。

我的矩阵类由:

#include<iostream>
#include <stdlib.h>
using namespace std;
class dymatrix
{
    friend ostream & operator << (ostream &os, const dymatrix &om);
    friend istream & operator >> (istream &is, dymatrix &om);
private:
    int rows;
    int columns;
    double *matrix;
public:
    dymatrix(){cout<<"Default constructor called"<<endl; columns = 0; rows=0; matrix=0;}
    ~dymatrix(){cout<<"Destructor called"<<endl;delete[] matrix;}  
    dymatrix(int inrows, int incolumns) //Parametrised objects, matrix database is defined here to store data.
    {
        rows = inrows;
        columns = incolumns;
        matrix = new double [inrows*incolumns];
        for (int i=0; i<inrows*incolumns; i++) 
        { 
            matrix[i]=0;
        }
    }
    int lengthr() const {return rows;}  //Returns number of rows.
    int lengthc() const {return columns;}   //Return number of columns.
    dymatrix &operator=( dymatrix &arr); //This is the assignment member function.
    dymatrix(dymatrix&);    //This is the deep copy member function.
    dymatrix operator*(const dymatrix& arr)const ;  //Overloading "*" operator.

    double & operator[](const int n)    //Overloading "[]" operator, this is important !!!
    {
        if(n<0 || n>=rows*columns)
        {
            cout<<"Error: trying to access matrix element out of bounds"<<endl;
            exit(1);
        }
    return matrix[n];
    }
    int index(int j, int i) const //This member function returns the position of each index.
    {
        if (j > 0 && j <=rows && i > 0 && i <=columns)
        {
        //cout<<"i is "<<i<<" j is "<<j<<endl<<endl<<"row is "<<rows<<" columns is "<<columns<<endl;
            return (i-1)+(j-1)*columns;
        }
        else {cout<<"Error, out of range"<<endl<<"i is "<<i<<" j is "<<j<<endl<<endl<<"row is "<<rows<<" columns is "<<columns<<endl; exit (1);}
    }
    double & operator()(int j, int i) const {return matrix[index(j,i)];} //The operator () returns the position of j and i in 1D array.
    }; //Class End.

其中“index”成员函数将矩阵中每个元素的位置返回到一维数组中:

int index(int j, int i) const //This member function returns the position of each index.
    {
        if (j > 0 && j <=rows && i > 0 && i <=columns)
        {
        //cout<<"i is "<<i<<" j is "<<j<<endl<<endl<<"row is "<<rows<<" columns is "<<columns<<endl;
            return (i-1)+(j-1)*columns;
        }
        else {cout<<"Error, out of range"<<endl<<"i is "<<i<<" j is "<<j<<endl<<endl<<"row is "<<rows<<" columns is "<<columns<<endl; exit (1);}
    }
    double & operator()(int j, int i) const {return matrix[index(j,i)];}  //The operator () returns the position of j and i in 1D array.

这是我在类外重载乘法“*”运算符的部分:

dymatrix dymatrix:: operator * (const dymatrix &arr) const //Overloading "*" operator.
{
    if (columns != arr.rows)
    {
        cerr<<"SIZE DO NOT MATCH, YOU FAIL"<<endl; exit(1);
    }
    dymatrix new_matrix(rows,arr.columns);
    for (int j = 1; j <= rows; j++)
    {
        for (int i = 1; i <= arr.columns; i++)
        {
            for (int k = 1; k <= columns; k++)
            {
                new_matrix.matrix[index(j,i)]= new_matrix.matrix[index(j,i)]+ matrix[index(j,k)]*arr(k,i);
                cout<<"new_matrix = "<<new_matrix<<endl<<endl;
            }
        }
    }
    return new_matrix;
}

这里给出了 int main:

int main()
{
    dymatrix a1;
    cin >> a1;  //Define the rows of the matrix
    cout << a1<<endl<<endl;
    dymatrix a2;
    cin >> a2;
    cout << a2<<endl<<endl;
    dymatrix resu_a3;
    resu_a3 = a1*a2;
    cout<<"Multiplication = "<<resu_a3<<endl;
    return 0;
}

所以我在运行代码后得到的错误消息是我自己在“index”成员函数中编写的错误消息:

“错误，超出范围”。

此错误消息表明 i 和 j 分别小于 0 或大于现有列数和行数，我不明白为什么会这样。

我的完整代码在这里:

#include<iostream>
#include <stdlib.h>
using namespace std;
class dymatrix
{
    friend ostream & operator << (ostream &os, const dymatrix &om);
    friend istream & operator >> (istream &is, dymatrix &om);
private:
    int rows;
    int columns;
    double *matrix;
public:
    dymatrix(){cout<<"Default constructor called"<<endl; columns = 0; rows=0; matrix=0;}
    ~dymatrix(){cout<<"Destructor called"<<endl;delete[] matrix;}  
    dymatrix(int inrows, int incolumns) //Parametrised objects, matrix database is defined here to store data.
    {
        rows = inrows;
        columns = incolumns;
        matrix = new double [inrows*incolumns];
        for (int i=0; i<inrows*incolumns; i++) 
        { 
            matrix[i]=0;
        }
    }
    int lengthr() const {return rows;}  //Returns number of rows.
    int lengthc() const {return columns;}   //Return number of columns.
    dymatrix &operator=( dymatrix &arr); //This is the assignment member function.
    dymatrix(dymatrix&);    //This is the deep copy member function.
    dymatrix operator*(const dymatrix& arr)const ;  //Overloading "*" operator.

    double & operator[](const int n)    //Overloading "[]" operator, this is important !!!
    {
        if(n<0 || n>=rows*columns)
        {
            cout<<"Error: trying to access matrix element out of bounds"<<endl;
            exit(1);
        }
    return matrix[n];
    }
    int index(int j, int i) const //This member function returns the position of each index.
    {
        if (j > 0 && j <=rows && i > 0 && i <=columns)
        {
        //cout<<"i is "<<i<<" j is "<<j<<endl<<endl<<"row is "<<rows<<" columns is "<<columns<<endl;
            return (i-1)+(j-1)*columns;
        }
        else {cout<<"Error, out of range"<<endl<<"i is "<<i<<" j is "<<j<<endl<<endl<<"row is "<<rows<<" columns is "<<columns<<endl; exit (1);}
    }
    double & operator()(int j, int i) const {return matrix[index(j,i)];} //The operator () returns the position of j and i in 1D array.
}; //Class End.
    dymatrix::dymatrix(dymatrix &arr)   //This is the copy constructor for deep copying.
    {
        matrix = 0; rows = arr.lengthr(); columns = arr.lengthc();
        if (rows*columns >0)
        {
            matrix = new double [rows*columns];
            for (int i =0; i < rows*columns; i++) 
            {
                matrix[i] = arr[i];
            }
        }
    }
    dymatrix & dymatrix ::operator = (dymatrix &arr)
    {
        if(&arr == this) return *this; // no self assignment
        delete[] matrix; matrix=0; rows=columns=0;
        rows=arr.lengthr();
        columns = arr.lengthc();
        if(rows*columns>0)
         {
            matrix=new double[rows*columns];
            // Copy values into new array
            for(int i=0;i<rows*columns;i++) matrix[i] = arr[i];
        }
    return *this; // Special pointer!!
    }
    istream & operator >> (istream &is, dymatrix &om)   //Overloading ">>" operator here to
    {
        cout<<"Please enter the number of rows you want"<<endl;
        is >> om.rows;  //Inputting number of rows.
        cout<<"Enter the number of columns you want"<<endl;
        is >> om.columns;   //Inputting number of columns.
        cout<<"Enter matrix"<<endl;
        om.matrix = new double [om.rows*om.columns];    //Making a dynamic array here to put the data in.
        for (int j = 1; j <= om.rows; j++)
        {
            for (int i = 1; i <= om.columns; i++)
            {
                is >> om.matrix[om.index(j,i)]; //Putting in the data into this dynamic array for each element.
            }
        }
        return is;
    }
    ostream & operator << (ostream &os, const dymatrix &om)  //To output the matrix in an standard matrix way
    {
        for(int j= 1; j<=om.rows; j++)
        {
            os<<endl<<endl;
            for (int i = 1; i <=om.columns;i++)
            {
                os << om.matrix[om.index(j,i)]<<"\t";   //Similar method used in istream.
            }
        }
        return os;
    }

    dymatrix dymatrix:: operator * (const dymatrix &arr) const //Overloading "*" operator.
    {
        if (columns != arr.rows)
        {
            cerr<<"SIZE DO NOT MATCH, YOU FAIL"<<endl; exit(1);
        }
        dymatrix new_matrix(rows,arr.columns);
        for (int j = 1; j <= rows; j++)
        {
            for (int i = 1; i <= arr.columns; i++)
            {
                for (int k = 1; k <= columns; k++)
                {
                    new_matrix.matrix[index(j,i)]= new_matrix.matrix[index(j,i)]+ matrix[index(j,k)]*arr(k,i);
                    cout<<"new_matrix = "<<new_matrix<<endl<<endl;
                    cout<<"k "<<k<<endl<<" arr.columns is "<<arr.columns<<endl<<"columns is "<<columns<<endl<<endl;
                }
            }
        }
        return new_matrix;
    }

int main()
{
    dymatrix a1;
    cin >> a1;  //Define the rows of the matrix
    cout << a1<<endl<<endl;
    dymatrix a2;
    cin >> a2;
    cout << a2<<endl<<endl;
    dymatrix resu_a3;
    resu_a3 = a1*a2;
    cout<<"Multiplication = "<<resu_a3<<endl;
    return 0;
}

Answer 1

在您的乘法运算符代码中，这一行是错误的:

new_matrix.matrix[index(j,i)]= new_matrix.matrix[index(j,i)]+ matrix[index(j,k)]*arr(k,i);

问题是 index(j,i) 实际上是 this->index(j,i)，而不是 new_matrix.index(j, i) 如你所料...

您应该将其替换为:

new_matrix(j,i) += matrix[index(j,k)]*arr(k,i);

但真正的问题是:您是否有充分的理由实现自己的矩阵类，而不是使用像 Armadillo 这样经过实战检验的矩阵库？