Question

我正在使用

scipy.linalg import eigh

计算特征值。但是，在计算非正特征值时，一切工作正常。Scipy提供的结果与Cpp中的特征库不同。

我在2 Cpp和Python上尝试了相同的数组数据。非阴性结果似乎是正确的。但不是负面的。

'''python

    from scipy.linalg import eigh
    eigenVal, eigenVec = eigh(XtX)
    idx = eigenVal.argsort()[::-1]
    eigenVal = eigenVal[idx] / n  # Descending Sort

'''

'''Cpp

   // Compute Eigendecomposition:
   Eigen::MatrixXf XtX (r,r);
   if (m <= n
        XtX.template triangularView<Eigen::Lower>() = X * X.transpose();
   else
        XtX.template triangularView<Eigen::Lower>() = X.transpose() * X;
   Eigen::SelfAdjointEigenSolver<Eigen::MatrixXf> eig (XtX);
   // eigenvalues provide squared singular values:
   Eigen::VectorXf s = eig.eigenvalues();

   s=s.reverse().eval()/n;

'''

python中的

输出： '''

array([  1.97322578e+05,   8.04158203e+03,   7.24907227e+03,           
    6.59655957e+03,   5.78095068e+03,   5.29064844e+03,
    4.74032520e+03,   4.46454346e+03,   4.23509229e+03,
    4.09968652e+03,   3.52356104e+03,   3.17308252e+03,
    3.14735107e+03,   2.88025342e+03,   2.80748145e+03,
    2.62388794e+03,   2.50723022e+03,   2.42145996e+03,
    2.11814282e+03,   2.03532385e+03,   1.79338770e+03,
    1.75364771e+03,   1.69037793e+03,   1.57554895e+03,
    1.45615894e+03,   1.33216003e+03,   1.26516211e+03,
    1.18433081e+03,   1.14839172e+03,   9.90758057e+02,
    8.59174011e+02,   8.20709900e+02,   7.86408569e+02,
    7.27681091e+02,   6.52041077e+02,   5.90487732e+02,
    5.26059814e+02,   4.99097687e+02,   4.49730896e+02,
    4.16578094e+02,   3.22004700e+02,   3.04409729e+02,
    2.79609161e+02,   2.15276245e+02,   1.84194916e+02,
    1.57032639e+02,   1.26647469e+02,   9.45600433e+01,
    7.59200439e+01,   5.26064911e+01,   4.35399475e+01,
    3.20723610e+01,   2.21866665e+01,   1.30586596e+01,
    3.81547445e-03,   1.16530398e-03,   1.07570493e-03,
    9.38778510e-04,   7.38311443e-04,   5.67958807e-04,
    5.35471656e-04,   5.30579535e-04,   5.17265638e-04,
    5.16666041e-04,   5.10115584e-04,   5.03800577e-04,
    5.00108406e-04,   4.70151805e-04,   4.33832814e-04,
    4.32742119e-04,   4.15480201e-04,   3.78245371e-04,
    3.75256117e-04,   3.71288595e-04,   3.53171228e-04,
    3.44453088e-04,   3.06655653e-04,   3.04728514e-04,
    2.60292058e-04,   2.57157430e-04,   2.02826763e-04,
    1.92918960e-04,   1.73933528e-04,  -9.30694770e-03], 
dtype=float32)$

在C中的输出：

    197323     8041.61    7249.11    6596.59    5780.98    5290.66    
    4740.34    4464.56    4235.1    4099.7    3523.58    3173.09
    3147.36    2880.26    2807.48    2623.89    2507.23    2421.46
    2118.15    2035.33    1793.39    1753.65    1690.38    1575.55
    1456.16    1332.16    1265.16    1184.33    1148.39    990.759
    859.177    820.711    786.409    727.682    652.043    590.488
    526.061    499.099    449.731    416.578    322.005     304.41
    279.611    215.276    184.195    157.033    126.647    94.5601
    75.9213    52.6073    43.5399    32.0722    22.1875    13.0586
    0.0208003    0.00212419    0.00183017    0.00154398    
    0.00125332   0.00120334    0.00113175    0.000939068  
    0.000862687  0.000722841     0.000684395  0.000629895  
    0.000528611  0.000499585  0.0004829     0.000405769  0.000357388  
    0.000167705  8.70496e-05 -1.52459e-05     -0.000112141  
    -0.000141369  -0.000237786  -0.000504876  -0.000550637     
    -0.000704483  -0.000729621  -0.000882211  -0.00105727  -0.00215314

Answer 1

您正在使用单精度浮点数。它们的相对精度约为1e-7，因此所有低于197323 * 1e-7的特征值都可以视为零。考虑到这一点，可以认为两个版本在数值上都是等效的。要获得更高的准确性，请切换为双精度。

在非阳性组件中使用不同于Cpp中本征库的python计算本征值

1 个答案: