cholrot.cholsolve

cholrot.cholsolve(R, z, b, *, alpha=-1, lower=False, check=True)

Solve (A + alpha*z*z.T) x = b without forming the modified matrix.

The base SPD matrix A is represented by the Cholesky factor R:

  • A = R.T @ R for an upper factor (lower=False), or

  • A = R @ R.T for a lower factor (lower=True).

The computation uses the rank-one inverse identity and triangular solves with the original factor. It does not materialize A + alpha*z*z.T or the modified Cholesky factor.

Parameters:

  • R (ndarray)

  • z (ndarray)

  • b (ndarray)

  • alpha (float)

  • lower (bool)

  • check (bool)

Return type:

ndarray