Solves one or more linear systems or least-squares problems.

[dst,ret] = cv.solve(src1, src2)
[...] = cv.solve(..., 'OptionName', optionValue, ...)

Input

• src1 input matrix on the left-hand side of the system.
• src2 input matrix on the right-hand side of the system.

Output

• dst output solution.
• ret Logical return value, see below.

Options

• Method solution (matrix inversion) method, default 'LU'. One of the following matrix decomposition types:
  • LU Gaussian elimination with the optimal pivot element chosen.
  • SVD singular value decomposition (SVD) method; the system can be over-defined and/or the matrix src1 can be singular
  • EIG eigenvalue decomposition; the matrix src1 must be symmetrical
  • Cholesky Cholesky LLT factorization; the matrix src1 must be symmetrical and positively defined
  • QR QR factorization; the system can be over-defined and/or the matrix src1 can be singular
• IsNormal this flag can be used together with any of the previous methods; it means that the normal equations src1' * src1 * dst = src1' * src2 are solved instead of the original system src1 * dst = src2. defaul false

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

dst = argmin_{X} ||src1*X - src2||

If 'LU' or 'Cholesky' method is used, the function returns 1 if src1 (or src1'*src1) 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.

Note

If you want to find a unity-norm solution of an under-defined singular system src1 * dst = 0, the function cv.solve will not do the work. Use cv.SVD.SolveZ instead.