PSCOILS

PSCOILS combines the sequence and the profile information using a linear weighting scheme, namely $\lambda COILS + (1-\lambda)PCOILS$ with $\lambda$ in the range of $[0,1]$ the only variation with respect to the previous algorithm is again the $f$ equation (5 and 7). We then have as before

$$x_i=(\prod_{h=1}^W f(S,P,h,\lambda)^{e_h})^{1/N}$$ (8)

and

$$f(S,P,h,\lambda)=\lambda S^h(a_{i+h}) + (1-\lambda) <S^h,P_{i+h}>$$ (9)

where the meaning of $S^h(a_{i+h})$ and $<S^h,P_{i+h}>$ are the same as in 5 and 7, respectively. No attempt have been made to optimize $\lambda$ but in the current stage it has been set to $1/2$. In this case the sequence and the profile are equally weighted.