D.13.1 minpack calling conventions

The minpack library solves a similar problem to that of the kinsol library (kinsol), and the two libraries have identical calling conventions at the level of the virtual code interface.

The hybrd and lmdif functions take input arguments of the form (f,(i,o)), whereas hybrj, lmder, and lmstr take arguments of the form ((f,j),(i,o)). The interpretations of these parameters are explained in kinsol input parameters.

For the lmstr function, the Jacobian function j takes an argument (m,v) and returns only the m-th row of the Jacobian matrix. For lmder and hybrj, the Jacobian function takes only an input vector v and returns the whole matrix. These specifications are also explained further in relation to the kinsol library.

The output from any minpack function is a vector v satisfying f(v) = o to the best possible tolerance if a solution is found. A range of tolerances over ten orders of magnitude is sampled starting from 1e-15. If no solution is found, an empty list is returned.