free() 动态数组时出现 double free 错误。

Question

在 free(Hk) 时出现错误 “Error in `./test': double free or corruption (out): 0x00000000011c6f30"。看不出哪里错了。

代码：

void linalg::sp_Davidson(const char uplo, const SparseMatrix_COO& a, double* diagValsA, double* eigVecs, double* eigVals, int nroot, int p, double tol, int MaxCycle, int MaxSpace, std::ostream& os)
{
    int n = a.nRows(); // the size of matrix a
    // workspaces
    double* Vk = (double*)std::malloc(sizeof(double) * (n * MaxSpace));
    double* Wk = (double*)std::malloc(sizeof(double) * (n * MaxSpace));
    double* Hk = (double*)std::malloc(sizeof(double) * (MaxSpace * MaxSpace));
    double* Sk = (double*)std::malloc(sizeof(double) * (MaxSpace)); // eigenvals of Hk
    double* Sold = (double*)std::malloc(sizeof(double) * nroot);
    double* Q1 = (double*)std::malloc(sizeof(double) * n);
    double* Q2 = (double*)std::malloc(sizeof(double) * n);
    // generate initial guess Vk
    std::memset(Vk, 0, (sizeof(double) * n * p));
    for(int i = 0; i < p; ++i) Vk[i * n + i] = 1.0;
    // iterative diagonalization
    int ispace = p; // current subspace size
    int k = 0; // cycle count
    while(k < MaxCycle)
    {
        os << "--> k: " << k << std::endl;
        // current space size
        os << "ispace: " << ispace << std::endl;
        // MGS(Vk)
        MGS(Vk, n, ispace);
        // compute W_k = A V_k, size: [n, ispace] = [n, n] * [n, ispace]
        sp_coosymm(uplo, a, Vk, ispace, Wk);
        // compute H_k = V_K^T A V_k = V_K^T W_k
        cblas_dgemm(CblasColMajor, CblasTrans, CblasNoTrans, ispace, ispace, n, 1.0, Vk, n, Wk, n, 0.0, Hk, ispace);
        // Sk, Hk = eig(Hk)
        LAPACKE_dsyevd(LAPACK_COL_MAJOR, 'V', 'U', ispace, Hk, ispace, Sk);
        // compute eigenvecs eigVecs = Vk * Hk[:p], size: [n, p] = [n, ispace] * [ispace, p], Ritz approximations
        cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, n, p, ispace, 1.0, Vk, n, Hk, ispace, 0.0, eigVecs, n);
        double norm = 9999.0;
        for(int j = 0; j < p; ++j)
        {
            // Q1 = Wk*Hk[j] - S[j]*Vk*Hk[j]
            // Q1 = Wk*Hk[j]
            cblas_dgemv(CblasColMajor, CblasNoTrans, n, ispace, 1.0, Wk, n, (Hk + j * ispace), 1, 0.0, Q1, 1);
            // Q2 = Vk*Hk[j]
            cblas_dgemv(CblasColMajor, CblasNoTrans, n, ispace, 1.0, Vk, n, (Hk + j * ispace), 1, 0.0, Q2, 1);
            // Q1 = - Sk[j]*Q2 + Q1
            cblas_daxpy(n, -Sk[j], Q2, 1, Q1, 1);
            // Q1 = Q1 / (Sk[j] - A[j][j])
            cblas_dscal(n, (Sk[j] - diagValsA[j]), Q1, 1);
            // V[:,ispace] = q1
            cblas_dcopy(n, Q1, 1, (Vk + n * ispace), 1);
            ++ispace;
            if(ispace >= MaxSpace) // restart
            {
                ispace = p;
                break;
            }
        }
        // compute norm for n root
        // Sold = -Sk + Sold
        cblas_daxpy(nroot, -1.0, Sk, 1, Sold, 1);
        norm = cblas_dnrm2(nroot, Sold, 1);
        // Sold = Sk
        cblas_dcopy(nroot, Sk, 1, Sold, 1);
        if(norm < tol)
        {
            break;
        }
        ++k;
    }
    if(k < MaxCycle)
    {
        os << "------> convergence reached! <------" << std::endl;
        os << "--> nloop: " << k << std::endl;
    }
    else
    {
        os << "------> unconverged! <------" << std::endl;
    }
    cblas_dcopy(nroot, Sold, 1, eigVals, 1);
    std::free(Q2);
    std::free(Q1);
    std::free(Sold);
    std::free(Sk);
    std::free(Hk);
    std::free(Wk);
    std::free(Vk);
}

因为 MaxSpace 比较大，过程中不会有越界问题。那么对 Hk 数组的 free 究竟有什么问题？

感谢解答。

Answer 1

分配内存要检查返回值, 否则你怎么确认你都分配成功了呢?
类似

    double* Vk = (double*)std::malloc(sizeof(double) * (n * MaxSpace));
    ...
    if(Vk && Wk && ...){
      ....
    }