At the beginning of step i, the variable Xk (var_id, var_name) either enters into (positive var_id) or drops from (negative var_id) the regression model, and the current common correlation between active variables and current residuals is max_abs_corr.
After moving along the equiangular direction for step_length distance, either an inactive variable qualifies to enter into the model or a currently active variable is dropped from the model, in which the process reaches step i+1, so the intercept and coefficients correspond to the end of step i as well as the beginning of step i+1.