Solve linear least-square problem using OpenCV (Reference)

C++: bool solve(InputArray src1, InputArray src2, OutputArray dst, int flags=DECOMP_LU)

Parameters:

• src1 – input matrix on the left-hand side of the system.

• src2 – input matrix on the right-hand side of the system.

• dst – output solution.

• flags –

solution (matrix inversion) method.

• DECOMP_LU Gaussian elimination with optimal pivot element chosen.

• DECOMP_CHOLESKY Cholesky  factorization; the matrix src1 must be symmetrical and positively defined.

• DECOMP_EIG eigenvalue decomposition; the matrix src1 must be symmetrical.

• DECOMP_SVD singular value decomposition (SVD) method; the system can be over-defined and/or the matrixsrc1 can be singular.

• DECOMP_QR QR factorization; the system can be over-defined and/or the matrix src1 can be singular.

• DECOMP_NORMAL while all the previous flags are mutually exclusive, this flag can be used together with any of the previous; it means that the normal equations  are solved instead of the original system  .

The function solve solves a linear system or least-squares problem (the latter is possible with SVD or QR methods, or by specifying the flag DECOMP_NORMAL ):

If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1 if src1 (or  ) is non-singular. Otherwise, it returns 0. In the latter case, dst is not valid. Other methods find a pseudo-solution in case of a singular left-hand side part.

In my case, I have equation min|| P*b - (Xnew - Xm) || to solve. P is mxp eigenvector, Xnew is the target shape, Xm is the mean shape in trained model, b is the shape parameter vector we want to get. m is number of attributes (number of point * 3), p is the number of reduced eigenvalue.

Reference: http://docs.opencv.org/modules/core/doc/operations_on_arrays.html#solve