0

我有问题。

我已经用 C++ 编写了相当多的代码。我正在使用 MS Visual Studio 2010。

这是一个matrix几乎没有简单数值函数的类。

以下是实现：

//matrix.h
#pragma once
#define EPS pow(10., -12.)

#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

class matrix
{
private:
    unsigned int n;     //number of columns
    unsigned int m;     //number of rows
    double* T;
public: 
    matrix ();
    matrix (unsigned int _n);
    matrix (unsigned int _n, unsigned int _m);
    ~matrix ();
    matrix (const matrix& A);
    matrix operator = (const matrix& A);

    unsigned int size_n () const;
    unsigned int size_m () const;

    void ones ();
    void zeros ();
    void identity ();

    void push (unsigned int i, unsigned int j, double v);

    void lu ();
    void gauss ();
    double det ();
    void transposition ();
    void inverse ();
    bool symmetric ();
    bool diag_strong_domination ();

    void swap_rows (unsigned int i, unsigned int j);

    matrix gauss_eq (matrix b);

    friend bool operator == (const matrix A, const matrix B);

    friend matrix operator + (const matrix A, const matrix B);

    friend matrix operator * (const matrix A, const matrix B);

    double operator () (unsigned int i, unsigned int j) const;

    friend ostream& operator << (ostream& out, const matrix& A);
};

matrix::matrix () : n(0), m(0)
{    
    this->T = NULL;
}


matrix::matrix (unsigned int _n) : n(_n), m(_n)
{    
    if (0==_n)
    {
        this->T = NULL;
        return;
    }

    this->T = new double [(this->n)*(this->m)];

    for (unsigned int i=0; i<this->n*this->m; i++)
        this->T[i] = (double)0;
}


matrix::matrix (unsigned int _n, unsigned int _m) : n(_n), m(_m)
{
    if (0==_m || 0==_n)
        throw "Error: Wrong matrix dimensios";

    this->T = new double [n*m];

    for (unsigned int i=0; i<n*m; i++)
        this->T[i] = (double)0;
}


matrix::~matrix ()
{
    delete this->T;
}


matrix::matrix (const matrix& A) : n(A.n), m(A.m)
{
    this->T = new double [n*m]; //(double*)malloc(A.m*A.n*sizeof(double));

    for (unsigned int i=0; i<n*m; i++)
        this->T[i] = A.T[i];
}


matrix matrix::operator= (const matrix& A)
{
    if (!(*this==A))
    {
        this->m = A.m;
        this->n = A.n;

        delete this->T;
        this->T = new double [A.n*A.m];

        for (unsigned int i=0; i<A.n*A.m; i++)
            this->T[i] = A.T[i];
    }

    return *this;
}



unsigned int matrix::size_n () const
{
    return this->n;
}

unsigned int matrix::size_m () const
{
    return this->m;
}

void matrix::ones ()
{
    for (unsigned int i=0; i<(this->m)*(this->m); i++)
        (*this).T[i] = double(1);

    return;
}

void matrix::zeros ()
{
    for (unsigned int i=0; i<(this->m)*(this->m); i++)
        (*this).T[i] = double(0);

    return;
}

void matrix::identity ()
{
    if (this->m!=this->n)
        throw "Error: Matrix have to be square (identity)";

    for (unsigned int i=0; i<(this->m)*(this->m); i++)
        (*this).T[i] = double(0);

    for (unsigned int k=1; k<=this->m; k++)
        (*this).push(k, k, (double)1);

    return;

}

void matrix::push (unsigned int i, unsigned int j, double v)
{
    if (i<=0 || i>this->m || j<=0 || j>this->n)
        throw "Error: Indeks out of range (push)";

    this->T[(i-1)*this->n + (j-1)] = v;
}


void matrix::lu ()
{
    if (this->m!=this->n)
        throw "Error: Matrix have to be square (lu)";

    if ((*this).diag_strong_domination())
    {
        //Doolittle decomposition
        matrix L(this->m);
        matrix U(this->m);

        for (unsigned int b=1; b<=this->m; b++)
            L.push(b, b, (double)1);

        for (unsigned int b=1; b<=this->m; b++)
            U.push(1, b, (*this)(1,b));

        for (unsigned int b=2; b<=this->m; b++)
        {
            for (unsigned int c=1; c<=this->m; c++)
            {
                for (unsigned int k=1; k<=b-1; k++)
                {
                    double s1 = 0;

                    if (1==k)
                        s1 = (double)0;

                    else
                        for (unsigned int p=1; p<=k-1; p++)
                            s1 += L(b,p) * U(p,k);

                    double v = ((*this)(b,k) - s1)/U(k,k);
                    L.push(b, k, v);
                }
                for (unsigned int k=b; k<=this->m; k++)
                {
                    double s2 = 0;

                    for (unsigned int p=1; p<=b-1; p++)
                        s2 += L(b,p) * U(p,k);

                    double v = (*this)(b,k) - s2;
                    U.push(b, k, v);
                }
            }
        }

        for (unsigned int p=1; p<=this->m; p++)
            L.push(p, p, (double)0);

        (*this) = L + U;

        for (unsigned int x=0; x<(*this).m*(*this).n; x++)
        {
            if (abs((*this).T[x])<EPS)
                (*this).T[x] = (double)0;
        }

        return;
    }

    (*this).gauss();

    return;
}


void matrix::gauss()
{
    //LU decomposition (gauss elimination with partal choice of main element)
    unsigned int n = (*this).m;
    matrix U(*this);
    matrix svr(1,n);
    for (unsigned int a=1; a<=n; a++)
        svr.push(a, 1, a);

    for (unsigned int k = 1; k<=(n-1); k++)
    {
        //main element choice - column
        unsigned int max = k;
        for (unsigned int q=k; q<=n; q++)
        {
            if (abs(U(q,k)) > abs(U(max,k)))
                max = q;
        }
        unsigned int p = max;
        svr.push(k, 1, p);


        if (abs(U(p,k)) < EPS)
            throw "Error: det = 0";

        //main element swap
        if (p!=k)
            U.swap_rows(p, k);

        //elimination
        for (unsigned int i=(k+1); i<=n; i++)
        {
            double tmp = U(i,k)/U(k,k);
            for (unsigned int j=(k+1); j<=n; j++)
            {
                double v = U(i,j) - tmp * U(k,j);
                U.push(i, j, v);
            }
        }
    }

    if (abs(U(n,n)) < EPS)
        throw "Error: det = 0";

    for (unsigned int s=2; s<=n; s++)
        for (unsigned int t=1; t<=(s-1); t++)
            U.push(s, t, (double)0);

    matrix T = (*this);
    matrix Uinv(U);
    Uinv.inverse();
    matrix L(n);

    for (unsigned int i=1; i<=n; i++)
        for (unsigned int j=1; j<=n; j++)
            for (unsigned int k=1; k<=n; k++)
            {
                double v = T(i,k) * Uinv(k,j);
                L.push(i, j, v);
            }

    //reversing rows swap
    for (unsigned int t=1; t<=n; t++)
    {
        if (t!=svr(t,1))
            L.swap_rows(t, svr(t,1));
    }

    (*this) = L + U;

    for (unsigned int k=1; k<=n; k++)
        (*this).push(k, k, (*this)(k,k) - (double)1);

    for (unsigned int x=0; x<(*this).m*(*this).n; x++)
    {
        if (abs((*this).T[x])<EPS)
            (*this).T[x] = (double)0;
    }

    return;
}


double matrix::det ()
{
    if (this->m!=this->n)
        throw "Error: Matrix have to be square (det)";

    double det = 1;
    matrix TMP = (*this);
TMP.lu();

for (unsigned int i=1; i<=this->m; i++)
        det *= (double)(TMP(i,i));

return det;
}


void matrix::transposition()
{
    matrix R(*this);

    for (unsigned int i=1; i<=(*this).m; i++)
        for (unsigned int j=1; j<=(*this).n; j++)
            (*this).push(j, i, R(i,j));

    return;
}


void matrix::inverse ()
{
    unsigned int n = (*this).m;

    matrix A(*this);
    matrix X(n);
    matrix b(1,n);

    for (unsigned int i=1; i<=n; i++)
    {
        b.zeros();
        b.push(i, 1, (double)1);

        X = A.gauss_eq(b); //error when using inverse in gauss function, used in lu

        for (unsigned int k=1; k<=n; k++)
            (*this).push(i, k, X(k,1));
        }

    for (unsigned int x=0; x<(*this).m*(*this).n; x++)
        if (abs((*this).T[x])<EPS)
            (*this).T[x] = (double)0;

    return; //error when calling inverse
}


bool matrix::diag_strong_domination()
{
    for (unsigned int i=1; i<=n; i++)
    {
        double s = (double)0;

        for (unsigned int j=1; j<=n; j++)
        {
            if (j!=i)
                s += abs((*this)(i,j));
        }

        if (s>=abs((*this)(i,i)))
            return false;
    }

    return true;
}


void matrix::swap_rows (unsigned int i, unsigned int j)
{
    if (i<=0 || i>this->m || j<=0 || j>this->n)
        throw "Error: Indeks out of range (swap_rows)";

    matrix R(*this);

    for (unsigned int p=1; p<=this->m; p++)
        for (unsigned int q=1; q<=this->n; q++)
        {
            if (p==i)
                (*this).push(p, q, R(j,q));
            if (p==j)
                (*this).push(p, q, R(i,q));
        }

    return;
}


matrix matrix::gauss_eq (matrix b)
{
    matrix A(*this);
    unsigned int n = this->m;

    for (unsigned int k=1; k<=n-1; k++)
    {
        unsigned int max = k;
        for (unsigned int q=k; q<=n; q++)
        {
            if (abs(A(q,k)) > abs(A(max,k)))
                max = q;
        }
        unsigned int p = max;

        if (abs(A(p,k)) < EPS)
            throw "Error: det = 0 (gauss_eq)";

        if (p!=k)
        {
            A.swap_rows(p,k);
            b.swap_rows(p,k);
        }

        for (unsigned int i=k+1; i<=n; i++)
        {
            double tmp = A(i,k) / A(k,k);
            for (unsigned int j=k+1; j<=n; j++)
                A.push(i, j, A(i,j) - tmp*A(k,j));
            b.push(i, 1, b(i,1) - tmp*b(k,1));
        }

        if (abs(A(n,n)) < EPS)
            throw "Error: det = 0 (gauss_eq)";
    }

    matrix X(1,n);

    double s = 0;

    for (unsigned int i=n; i>=1; i--)
    {
        for (unsigned int j=i+1; j<=n; j++)
            s = s + (A(i,j)*X(j,1));
        X.push(i, 1, (b(i,1)-s)/A(i,i));
        s = 0;
    }

    return X;
}


bool operator == (const matrix A, const matrix B)
{
    if (A.size_m()!=B.size_m() || A.size_n()!=B.size_n())
        return false;

    for (unsigned int i=1; i<=A.size_m(); i++)
        for (unsigned int j=1; j<=A.size_n(); j++)
            if (A(i,j)!=B(i,j))
                return false;

    return true;
}

matrix operator + (const matrix A, const matrix B)
{
    if (A.m!=B.m || A.n!=B.n)
        throw "Error: Wrong dimensions";

    matrix R(A.n, A.m);

    for (unsigned int i=0; i<A.m*A.n; i++)
        R.T[i] = A.T[i] + B.T[i];

    return R;
}

matrix operator * (const matrix A, const matrix B)
{
    if (A.n!=B.m)
        throw "Error: Wrong dimensions";

    matrix R(A.m,B.n);

    for (unsigned int i=1; i<=R.m; i++)
        for (unsigned int j=1; j<=R.n; j++)
            for (unsigned int k=1; k<=A.n; k++)
            {
                double v = R(i,j) + A(i,k) * B(k,j);
                R.push(i, j, v);
            }

    return R;
}

double matrix::operator () (unsigned int i, unsigned int j) const
{
    if (i<=0 || i>this->m || j<=0 || j>this->n)
        throw "Error: Indeks out of range (operator)";

    return this->T[(i-1)*this->n + (j-1)];
}

ostream& operator << (ostream& out, const matrix& A)
{
    if (0==A.size_m() || 0==A.size_n())
    {
        out<<endl<<" [  ]"<<endl;
        return out;
    }

    int s = 10;

    out<<endl<<" [ ";

    for (unsigned int i=1; i<=A.size_m(); i++)
    {
        for (unsigned int j=1; j<=A.size_n(); j++)
            out<<" "<<setw(s)<<left<<A(i,j)<<" ";

        if (i!=A.size_m())
            out<<endl<<"   ";
    }

    out<<" ] "<<endl;

    return out;
}

问题是我有关于记忆的奇怪错误。

首先，当我这样调用函数时inverse：

//MatLab.cpp

#include <iostream>
#include <complex>
#include <typeinfo>
using namespace std;

#include "matrix.h"

int main()
{
    try
    {
        matrix S(4);

        for (unsigned int i=1; i<=S.size_m(); i++)
            for (unsigned int j=1; j<=S.size_n(); j++)
            S.push(i, j, (double)3);

        for (unsigned int i=1; i<=S.size_m(); i++)
            S.push(i, i, (double)0);

        cout<<"S:"<<S<<endl;

        S.inverse();                     //<--- here is the problem
        cout<<endl<<"S^(-1) = "<<S<<endl;
    }
    catch (char* xcp)
    {
        cout<<endl<<xcp<<endl<<endl;
    }

    system("pause");
    return 0;
}

在函数中返回值时出现错误inverse。当我进入 destrutor 并在释放内存时出现错误。

然而，这还不是全部。

当我这样调用函数时，会出现另一种奇怪的情况lu：

//MatLab.cpp

#include <iostream>
#include <complex>
#include <typeinfo>
using namespace std;

#include "matrix.h"

int main()
{
    try
    {
        matrix S(4);

        for (unsigned int i=1; i<=S.size_m(); i++)
            for (unsigned int j=1; j<=S.size_n(); j++)
            S.push(i, j, (double)3);

        for (unsigned int i=1; i<=S.size_m(); i++)
            S.push(i, i, (double)0);

        cout<<"S:"<<S<<endl;

        S.lu();                                  //<--- here is the problem
        cout<<endl<<"LU decomposition"<<S<<endl;
    }
    catch (char* xcp)
    {
        cout<<endl<<xcp<<endl<<endl;
    }

    system("pause");
    return 0;
}

inverse在这种情况下，函数中使用的函数也会发生错误gauss，但这次是在将函数的结果分配gauss_eq给之前定义的矩阵时。

当我遇到这个问题时，我会去复制构造函数（我不知道为什么），我既不能用 new 运算符也不能用malloc函数分配内存。

当调试要执行的 nex 语句malloc.c在此函数的文件中时：

__forceinline void * __cdecl _heap_alloc (size_t size)

{

    if (_crtheap == 0) {
        _FF_MSGBANNER();    /* write run-time error banner */
        _NMSG_WRITE(_RT_CRT_NOTINIT);  /* write message */
        __crtExitProcess(255);  /* normally _exit(255) */
    }

    return HeapAlloc(_crtheap, 0, size ? size : 1);
}

参数大小等于 68。

我不知道有什么问题。

问题是在类矩阵中的构造函数或函数中，还是在我使用的 C 库中的函数中。

我希望有人花时间研究这个问题，尽管要查看很多代码。

感谢您的任何提示。

4

5 回答 5

2

您需要使用适当的管理类，而不是自己做。由于您已经进行了自己的 2D 索引，因此 astd::vector<double>将是一件好事。

于 2012-07-31T18:12:49.513 回答
2

我还没有阅读您的所有代码，但这绝对是错误的：

matrix::~matrix ()
{
    delete this->T;
}

你需要打电话给delete[]运营商，而不是普通的delete。 new必须始终与 匹配delete，并且new[]必须始终与 匹配delete[]。不这样做是未定义的行为，通常会导致某种内存损坏，从而使您的程序崩溃。

同样，您的实现也operator =应该调用delete[].

也不需要在每个成员访问前加上this->or (*this).。它不是惯用的 C++，只应在存在局部变量遮蔽成员变量的情况下使用（这本身并不总是好的做法）。

于 2012-07-31T18:10:50.823 回答
2

首先，方式，方式太多的代码。但是，问题很简单；你调用delete你分配的数组new []。用 分配的任何东西new[]都必须用 解除分配delete[]。你有同样的问题operator=。

于 2012-07-31T18:11:04.397 回答
0

你的赋值运算符是错误的，你写的地方

matrix matrix::operator=(const matrix& A)
{
    if (!(*this==A))

你实际上是想写

matrix& matrix::operator=(const matrix& A)
{
    if (this != &A)

您应该检查两个对象的地址是否不相等，而不是矩阵本身不相等（并且 operator= 应该返回一个引用）。

但无论如何，这种风格的赋值运算符是不好的。有一种更好的方法来编写赋值运算符，称为复制和交换习语。它不仅更正确，而且更容易编写。有关示例，请参见此处

http://programmingexamples.net/wiki/CPP/C%2B%2B0x/TheBigFive

于 2012-07-31T18:45:40.293 回答
0

好的。我做了一些改变，现在我像这样释放内存：

matrix::~matrix ()
{
    delete [] this->T;
}

和

matrix& matrix::operator= (const matrix& A)
{
    if (!(*this==A))
    {
        this->m = A.m;
        this->n = A.n;

        delete [] this->T;
        this->T = new double [A.n*A.m];

        for (unsigned int i=0; i<A.n*A.m; i++)
            this->T[i] = A.T[i];
    }

    return *this;
}

但它改变了任何东西，无论inverse是在自称还是在gauss.

在调试时我停在

extern "C" _CRTIMP int __cdecl _CrtIsValidHeapPointer(
        const void * pUserData
        )
{
        if (!pUserData)
            return FALSE;

        if (!_CrtIsValidPointer(pHdr(pUserData), sizeof(_CrtMemBlockHeader), FALSE))
            return FALSE;

        return HeapValidate( _crtheap, 0, pHdr(pUserData) );  /<-- here I stopped
}

在dbgheap.c.

于 2012-07-31T19:17:30.530 回答