Incorrect output from computeMatrixSqrt

[hengli]

The computeMatrixSqrt function in https://github.com/ethz-asl/Schweizer-Messer/blob/master/sm_eigen/include/sm/eigen/matrix_sqrt.hpp outputs incorrect results.

In contrast, the operatorSqrt function in the SelfAdjointEigenSolver class does the same work, but returns correct results.

[simonlynen]

@hengli Thanks for the heads up. Can you make a pull-request for that change. I would however prefer solving this via an LLT instead of using the EigenSolver which is terribly slow in Eigen.

[furgalep]

Hi Lionel, In what way are the results incorrect? Always? In a particular case?

[hengli]

Hi Paul,

I was applying the function to the precision matrix for both the odometry data and chessboard data, and the function failed each time, returning a triangular matrix, B where B != A * A^T and A is the precision matrix.

Here is an example precision matrix for the odometry data:
879853.40 -524626.08 190716.10
-524626.08 2665040.52 212751.35
190716.10 212751.35 3184398.77

The function returns the following result:
106.87 -330.05 871.49
119.22 1628.14 0.00
1784.49 0.00 0.00

[furgalep]

Maybe this was right all along:

In [4]: np.array([[106.87, -330.05, 871.49],[119.22, 1628.14, 0.00],[1784.49, 0.00, 0.00]])
Out[4]: 
array([[  106.87,  -330.05,   871.49],
       [  119.22,  1628.14,     0.  ],
       [ 1784.49,     0.  ,     0.  ]])

In [5]: U = np.array([[106.87, -330.05, 871.49],[119.22, 1628.14, 0.00],[1784.49, 0.00, 0.00]])

In [6]: np.dot(U,U.T)
Out[6]: 
array([[  879849.0195,  -524626.5656,   190708.4463],
       [ -524626.5656,  2665053.268 ,   212746.8978],
       [  190708.4463,   212746.8978,  3184404.5601]])

[HannesSommer]

Are you sure you checked it the right way? B != A * A^T is comletely normel (except some special cases), becaue the defining equation is A = BB^T. (for the Cholesky type square root B of A).