Returns an orthogonal matrix that diagonalizes both given matrices.

The given matrices must commute. Guarantees that the sorted diagonal matrix is not permuted by the diagonalization (except for nearly-equal values).

symmetric_matrix A real symmetric matrix.
diagonal_matrix A real diagonal matrix with entries along the diagonal sorted into descending order.
rtol Relative numeric error threshold.
atol Absolute numeric error threshold.
check_preconditions If set, verifies that the input matrices commute and are respectively symmetric and diagonal descending.

An orthogonal matrix P such that P.T @ symmetric_matrix @ P is diagonal and P.T @ diagonal_matrix @ P = diagonal_matrix (up to tolerance).

ValueError Matrices don't meet preconditions (e.g. not symmetric).