英特尔MKL LAPACKE_dsyevd，n> 32766 - >没有足够的内存来分配LAPACKE_dsyevd中的工作数组

Question

我想使用来自英特尔MKL（2019 Update 2）的LAPACKE_dsyevd计算实对称矩阵的所有特征值和所有特征向量。

我在C＃中使用以下方法：

public static class MKL
{
    public static double[,] SymmetricEig(double[,] a, out double[] w)
    {
        int n1 = a.GetLength(0);
        int n2 = a.GetLength(1);
        if (n1 != n2) throw new System.Exception("Matrix must be square");
        double[,] b = Copy(a);
        int matrix_layout = 101; // row-major arrays
        char jobz = 'V';
        char uplo = 'U';
        int n = n2;
        int lda = n;
        w = new double[n];
        _mkl.LAPACKE_dsyevd(matrix_layout, jobz, uplo, n, b, lda, w);
        return b;
    }
}

同

class _mkl
{
    [DllImport(DLLName, CallingConvention = CallingConvention.Cdecl, ExactSpelling = true, SetLastError = false)]
    internal static extern lapack_int LAPACKE_dsyevd(
        int matrix_layout, char jobz, char uplo, lapack_int n, [In, Out] double[,] a, lapack_int lda, [In, Out] double[] w);
}

以及以下测试代码：

    int n = 32766; // 32767 or greater --> Not enough memory to allocate work array in LAPACKE_dsyevd
    double[,] A = CreateRandomSymmetricMatrix(n);
    double[] w = new double[n];
    double[,] B = MKL.SymmetricEig(A, out w);

同

    static double[,] CreateRandomSymmetricMatrix(int n1)
    {
        double[,] m = new double[n1, n1];
        for (int i1 = 0; i1 < n1; i1++)
        {
            for (int i2 = 0; i2 <= i1; i2++)
            {
                m[i1, i2] = r.NextDouble();
                m[i2, i1] = m[i1, i2];
            }
        }
        return m;
    }

如果n大于32766则失败并显示以下错误消息：

内存不足以在LAPACKE_dsyevd中分配工作数组

我的电脑有128 GB的RAM就足够了。我知道<gcAllowVeryLargeObjects enabled="true" />，我把它设置为真。我很清楚C＃中多维数组的65535 ^ 2限制，请参阅2d-Array with more than 65535^2 elements --> Array dimensions exceeded supported range。

顺便说一下，我可以使用MATLAB为n = 40000或更大的矩阵计算特征值分解。我认为MATLAB也在使用英特尔MKL来计算它。

那么如何使用英特尔MKL计算C＃中非常大的矩阵（n> 40000）的特征值分解？

Answer 1

我不认为这是你的问题。以下定义表明w = new double[n];在你的情况下是小的方式。

*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If N <= 1,               LWORK must be at least 1.
*          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1.
*          If JOBZ = 'V' and N > 1, LWORK must be at least
*                                                1 + 6*N + 2*N**2.

你真的应该总是做一个工作区查询。我知道，文档会向用户公开，但它非常方便，有助于避免出现这种情况。所以你知道，如何进行工作区查询？如果没有真正快速击中我。

Answer 2

这似乎是LAPACKE_dsyevd的一个错误。使用LAPACKE_dsyevr也可以使用更大的矩阵。

我在MKL类中添加了以下行：

    public static double[,] SymmetricEigRelativelyRobustRepresentations(double[,] a, out double[] w)
    {
        int n1 = a.GetLength(0);
        int n2 = a.GetLength(1);
        if (n1 != n2) throw new System.Exception("Matrix must be square");
        double[,] b = Copy(a);
        int matrix_layout = 101; // row-major arrays
        char jobz = 'V'; // eigenvalues and eigenvectors are computed
        char range = 'A'; // the routine computes all eigenvalues
        char uplo = 'U'; // a stores the upper triangular part of A 
        int n = n2;
        int lda = n;
        int vl = 0;
        int vu = 0;
        int il = 0;
        int iu = 0;
        double abstol = 0;
        int m = n;
        w = new double[n];
        double[,] z = new double[n, n];
        int ldz = n;
        int[] isuppz = new int[2 * n];
        int info = _mkl.LAPACKE_dsyevr(matrix_layout, jobz, range, uplo, n, b, lda, vl, vu, il, iu, abstol, ref m, w, z, ldz, isuppz);
        return z;
    }

和以下几行到_mkl类：

    [DllImport(DLLName, CallingConvention = CallingConvention.Cdecl, ExactSpelling = true, SetLastError = false)]
    internal static extern lapack_int LAPACKE_dsyevr(
        int matrix_layout, char jobz, char range, char uplo, lapack_int n, [In, Out] double[,] a, lapack_int lda,
        double vl, double vu, lapack_int il, lapack_int iu, double abstol, [In, Out] ref lapack_int m, [In, Out] double[] w,
        [In, Out] double[,] z, lapack_int ldz, [In, Out] lapack_int[] isuppz);