# Parameter transformation (implicit) ```r Pimpl( trafo, parameters = NULL, condition = NULL, keep.root = TRUE, positive = TRUE, compile = FALSE, modelname = NULL, verbose = FALSE ) ``` ## Arguments - `trafo`: Named character vector defining the equations to be set to zero. Names correspond to dependent variables. - `parameters`: Character vector, the independent variables. - `condition`: character, the condition for which the transformation is generated - `keep.root`: logical, applies for `method = "implicit"`. The root of the last evaluation of the parameter transformation function is saved as guess for the next evaluation. - `positive`: logical, returns projection to the (semi)positive range. Comes with a warning if the steady state has been found to be negative. - `compile`: Logical, compile the function (see funC0 ) - `modelname`: Character, used if `compile = TRUE`, sets a fixed filename for the C file. - `verbose`: Print compiler output to R command line. ## Returns a function `p2p(p, fixed = NULL, deriv = TRUE)` representing the parameter transformation. Here, `p` is a named numeric vector with the values of the outer parameters, `fixed` is a named numeric vector with values of the outer parameters being considered as fixed (no derivatives returned) and `deriv` is a logical determining whether the Jacobian of the parameter transformation is returned as attribute "deriv". ## Details Usually, the equations contain the dependent variables, the independent variables and other parameters. The argument `p` of `p2p` must provide values for the independent variables and the parameters but ALSO FOR THE DEPENDENT VARIABLES. Those serve as initial guess for the dependent variables. The dependent variables are then numerically computed by multiroot . The Jacobian of the solution with respect to dependent variables and parameters is computed by the implicit function theorem. The function `p2p` returns all parameters as they are with corresponding 1-entries in the Jacobian. ## Examples ```r ######################################################################## ## Example 1: Steady-state trafo ######################################################################## f <- c(A = "-k1*A + k2*B", B = "k1*A - k2*B") P.steadyState <- Pimpl(f, "A") p.outerValues <- c(k1 = 1, k2 = 0.1, A = 10, B = 1) P.steadyState(p.outerValues) ######################################################################## ## Example 2: Steady-state trafo combined with log-transform ######################################################################## f <- c(A = "-k1*A + k2*B", B = "k1*A - k2*B") P.steadyState <- Pimpl(f, "A") logtrafo <- c(k1 = "exp(logk1)", k2 = "exp(logk2)", A = "exp(logA)", B = "exp(logB)") P.log <- P(logtrafo) p.outerValue <- c(logk1 = 1, logk2 = -1, logA = 0, logB = 0) (P.log)(p.outerValue) (P.steadyState * P.log)(p.outerValue) ######################################################################## ## Example 3: Steady-states with conserved quantitites ######################################################################## f <- c(A = "-k1*A + k2*B", B = "k1*A - k2*B") replacement <- c(B = "A + B - total") f[names(replacement)] <- replacement pSS <- Pimpl(f, "total") pSS(c(k1 = 1, k2 = 2, A = 5, B = 5, total = 3)) ``` ## See Also Pexpl for explicit parameter transformations

Pimpl function