java SVD JAMA 错误结果

Question

我有这个数组

double a[][] = {{1,1,1}, {0,1,1} , { 1,0,0}
        ,{0,1,0},{1,0,0},{1,0,1},{1,1,1},{1,1,1},{1,0,1},{0,2,0},{0,1,1}};

我想要获得 SVD(奇异值解压缩)，这是代码

Matrix A = new Matrix(a);
        SingularValueDecomposition s = A.svd();
        Matrix U = s.getU();
        Matrix S = s.getS();
        Matrix V = s.getV();

        Matrix K = U.times(S.times(V.inverse()));
        System.out.println("A=\n" + A);
        System.out.println("U=\n" + U);
        System.out.println("S=\n" + S);
        System.out.println("V=\n" + V);
        System.out.println("K=\n" + K);

我使用了 JAMA 库，得到了这些结果

U=
0.42012156898152025   -0.07479925424066838   -0.04597243910578701   
0.29948675880470416   0.20009225506128975   0.4078276625537902   
0.12063481017681585   -0.27489150930195816   -0.4538001016595771   
0.15756100229407313   0.3046476172068067   -0.2006466962808193   
0.12063481017681585   -0.27489150930195816   -0.4538001016595771   
0.2625605666874469   -0.379446871447475   0.15467425717503247   
0.42012156898152014   -0.0747992542406683   -0.04597243910578692   
0.42012156898152014   -0.0747992542406683   -0.04597243910578692   
0.2625605666874469   -0.379446871447475   0.15467425717503247   
0.31512200458814627   0.6092952344136134   -0.4012933925616386   
0.29948675880470416   0.20009225506128975   0.4078276625537902   

S=
4.098871971532176   0.0   0.0   
0.0   2.361570801317849   0.0   
0.0   0.0   1.2736686819384786   

V=
0.49446664222485476   -0.6491757618976977   -0.5779909773443018   
0.6458223761096932   0.7194469174866516   -0.2555574131873014   
0.581735505399926   -0.24691489036406603   0.7749947346102383 

但是V错了，应该是这样的

V= -0.49446664222485476 0.6491757618976977 -0.5779909773443018
-0.6458223761096932 0.7194469174866516 -0.2555574131873014
-0.581735505399926 0.24691489036406603 0.7749947346102383

这确实是一个拥抱错误，因为在 multibluein USV 之后我得到了这个 matirx，只需看看 E-16

K=
1.0000000000000013   1.0000000000000004   1.000000000000001   
4.996003610813204E-16   1.0   0.9999999999999998   
1.0000000000000002   -3.885780586188048E-16   8.881784197001252E-16   
-1.1102230246251565E-16   1.0000000000000002   1.3877787807814457E-16   
1.0000000000000002   -3.885780586188048E-16   8.881784197001252E-16   
1.0000000000000004   -5.551115123125783E-16   1.0000000000000004   
1.0000000000000009   1.0000000000000002   1.0000000000000007   
1.0000000000000009   1.0000000000000002   1.0000000000000007   
1.0000000000000004   -5.551115123125783E-16   1.0000000000000004   
-2.220446049250313E-16   2.0000000000000004   2.7755575615628914E-16   
4.996003610813204E-16   1.0   0.9999999999999998   

请帮帮我，我该怎么办，哪里错了，JAMA错了吗？!

Answer 1

结果看起来正确。在矩阵 K 中，像 1.0000000000000013 和 4.996003610813204E-16 这样的值分别[非常接近]1 和 0。这里发生了浮点错误，这就是数字略有偏差的原因。 Matlab 也做同样的事情。