Question

我在我的结构工程程序中发现了一个非常出色的软件包（MatNet）。但是，尽管MathNet严重依赖于Intel的MKL，但我看不到如何解决一般的本征问题以找到结构的本征频率。 Lapack有这个例程，所以MKL也应该有。为什么不使用MathNet？或者：MKL / Lapack例程似乎未暴露于C＃。任何人都可以指出正确的方向吗？

Answer 1

我终于找到了如何使用MathNet 4.5.1 / Intel MKL 2018-C解决广义特征问题的方法。

下面的示例演示了方法。

最后，MathNet与该问题没有多大关系。

MKL可以解决问题。您可以直接在MKL中调用FEAST例程。在下面的示例中，我将例程用于对称正定矩阵。

A和B都是这样的矩阵。

对于A和B，您都可以使用1D和2D矩阵。只需在下面的示例中剥离内部小卷发即可。

以下是一些代码：

static void testFEAST() {
Console.WriteLine("FEAST");
var B = new double[,] 
{
     { 13.3733 , 2.4521 , 3.3799 , 3.1977 , 2.9007 , 2.6071 , 3.3902 , 3.2255 , 2.9586 , 3.5153 } ,
     { 2.4521 , 12.1223 , 2.5726 , 2.2380 , 2.0391 , 2.1209 , 2.7328 , 2.3948 , 2.2053 , 2.7973 } ,
     { 3.3799 , 2.5726 , 13.7485 , 3.1880 , 2.8773 , 2.7257 , 3.5214 , 3.3768 , 3.1508 , 3.5774 } ,
     { 3.1977 , 2.2380 , 3.1880 , 14.1512 , 2.7701 , 2.7678 , 3.6396 , 3.5524 , 2.8490 , 3.8841 } ,
     { 2.9007 , 2.0391 , 2.8773 , 2.7701 , 12.9673 , 2.3737 , 2.8522 , 2.8937 , 2.4185 , 3.0515 },
     { 2.6071 , 2.1209 , 2.7257 , 2.7678 , 2.3737 , 12.6557 , 3.2495 , 2.7260 , 2.3528 , 2.9746 } ,
     { 3.3902 , 2.7328 , 3.5214 , 3.6396 , 2.8522 , 3.2495 , 14.3296 , 3.6048 , 3.1249 , 3.9598 } ,
     { 3.2255 , 2.3948 , 3.3768 , 3.5524 , 2.8937 , 2.7260 , 3.6048 , 13.5041 , 2.8991 , 3.7164 } ,
     { 2.9586 , 2.2053 , 3.1508 , 2.8490 , 2.4185 , 2.3528 , 3.1249 , 2.8991 , 12.7476 , 3.1122 } ,
     { 3.5153 , 2.7973 , 3.5774 , 3.8841 , 3.0515 , 2.9746 , 3.9598 , 3.7164 , 3.1122 , 14.3441 }
};

var A = new double[,]
{
     { 11.5799 , 1.7403 , 2.0762 , 2.1079 , 1.7030 , 1.5895 , 2.1214 , 2.2385 , 2.1249 , 1.8184 },
     { 1.7403 , 12.4871 , 3.0054 , 2.7232 , 2.3889 , 1.8735 , 2.7554 , 2.7438 , 2.7967 , 2.4238 },
     { 2.0762 , 3.0054 , 14.0486 , 3.4330 , 2.8362 , 2.5154 , 3.5907 , 3.1904 , 3.6474 , 3.0380 },
     { 2.1079 , 2.7232 , 3.4330 , 13.4159 , 2.6667 , 2.4686 , 3.3515 , 3.1004 , 3.3094 , 2.7956 },
     { 1.7030 , 2.3889 , 2.8362 , 2.6667 , 12.6734 , 1.6063 , 2.9022 , 2.6043 , 2.7512 , 2.3908 },
     { 1.5895 , 1.8735 , 2.5154 , 2.4686 , 1.6063 , 12.3309 , 2.4514 , 2.3327 , 2.5532 , 1.8412 },
     { 2.1214 , 2.7554 , 3.5907 , 3.3515 , 2.9022 , 2.4514 , 13.6878 , 3.0864 , 3.3708 , 2.8628 },
     { 2.2385 , 2.7438 , 3.1904 , 3.1004 , 2.6043 , 2.3327 , 3.0864 , 13.6752 , 3.2175 , 3.0414 },
     { 2.1249 , 2.7967 , 3.6474 , 3.3094 , 2.7512 , 2.5532 , 3.3708 , 3.2175 , 13.8028 , 2.7187 },
     { 1.8184 , 2.4238 , 3.0380 , 2.7956 , 2.3908 , 1.8412 , 2.8628 , 3.0414 , 2.7187 , 12.9621}
}; 

var fpm = new int[64];
fpm[0] = 1;  fpm[1] = 8;  fpm[2] = 12; fpm[3] = 20;  fpm[4] = 0;
fpm[5] = 0; fpm[13] = 0;  fpm[26] = 0;  fpm[27] = 1; fpm[63] = 0;            

double epsout = 0,emin = 0,emax = 10;

int N =10,
    lda = N,
    ldb = N,
    loop = 40,
    m0 = 10,
    m = 4,
    info = 0;
char uplo = 'F';
double[]  res = new double[N];
List<string> Errors = new List<string>();
double[] x = new double[N * m*20];
double[] Eigenvalues = new double[ m0];
try
{
    LAPACK.Init(fpm);
    LAPACK.EigenValuesFEAST(
           ref uplo, ref N, A, ref lda, /* stiffness*/
             B, ref ldb, /* mass */
              fpm, ref epsout, ref loop,
               ref emin, ref emax,
             ref m0, Eigenvalues,  x, ref m,  res, ref info);

    switch (info)
    {
        case 0: // all is well
            break;
        case 202:
           // there are a lot of error codes that need to be addressed...
           // see the web pages at Intel about FEAST
           break;
        default:
            if (info < -100)
                throw new ArgumentOutOfRangeException($"Error with argument #{-info - 100}" +
                    " of the Extended Eigensolver interface.");
            else
                if (info > 100)
                throw new ArgumentOutOfRangeException($"Problem with {info - 100}-th value of the" +
                    Environment.NewLine +
                    $"input Extended Eigensolver parameter(fpm[{info - 101}])." + Environment.NewLine +
                    "Only the parameters in use are checked.");
            break;
    }
    double[] Y = new double[] { 0.778167123908170 ,  0.920180634486485,   0.935607276067470 ,  // MathLab
      0.963915607694184 ,  0.985690628059698 ,
      1.015048284381503 ,  1.026313059366515 , 1.063031787597951  , 1.081547590133276,  1.212840409892686 };
    int round = 4;
    double maxError = double.MinValue;
    for (int i=0; i < m0; i++)
        if (Math.Round(Eigenvalues[i], round) != Math.Round(Y[i], round))
        {
            double error = Math.Abs((Eigenvalues[i] - Y[i]) / Y[i]);
            maxError = Math.Max(maxError, error);
            if (error > Math.Pow(10,round+1))
                throw new Exception($"Error in FEAST Eigenvalues[{i}] : Error =  {error * 100} % ");
        }

    Console.WriteLine($"FEAST OK, Max error {maxError:F2} %");
}
catch (BadImageFormatException bie)
{
       Debug.WriteLine(bie.Message + Environment.NewLine + "Probably an x86/x64 confusion");
}
catch (Exception ex)
    {
        Console.WriteLine(ex.Message);              
    }
}

public sealed class LAPACK
{
    string mkl = "mkl_rt.dll"; // make sure it is in your PATH
    [DllImport(mkl, CallingConvention = CallingConvention.Cdecl,   EntryPoint = "feastinit", ExactSpelling = true)]
    static public extern void Init(int[] fpm);
    [DllImport(mkl , CallingConvention = CallingConvention.Cdecl, EntryPoint = "dfeast_sygv", ExactSpelling = true)]
    static public extern void EigenValuesFEAST(ref char uplo, ref int n, double[,] a, ref int lda,
       double[,] b, ref int ldb,
       int[] fpm, ref double epsout, ref int loop,
       ref double emin, ref double emax,
       ref int m0, double[] e, double[] x, ref int m, double[] res, ref int info);
}

我生成矩阵并用MatLab检查结果

使用mathnet解决一般特征问题

1 个答案: