### 36.2 Initializing the Solver

The following functions initialize a multidimensional solver, either with or without derivatives. The solver itself depends only on the dimension of the problem and the algorithm and can be reused for different problems.

Function: gsl_multiroot_fsolver * gsl_multiroot_fsolver_alloc (const gsl_multiroot_fsolver_type * T, size_t n)

  This function returns a pointer to a newly allocated instance of a solver of type T for a system of n dimensions. For example, the following code creates an instance of a hybrid solver, to solve a 3-dimensional system of equations.

      const gsl_multiroot_fsolver_type * T
          = gsl_multiroot_fsolver_hybrid;
      gsl_multiroot_fsolver * s
          = gsl_multiroot_fsolver_alloc (T, 3);

  If there is insufficient memory to create the solver then the function returns a null pointer and the error handler is invoked with an error code of `GSL_ENOMEM`.

Function: gsl_multiroot_fdfsolver * gsl_multiroot_fdfsolver_alloc (const gsl_multiroot_fdfsolver_type * T, size_t n)

  This function returns a pointer to a newly allocated instance of a derivative solver of type T for a system of n dimensions. For example, the following code creates an instance of a Newton-Raphson solver, for a 2-dimensional system of equations.

      const gsl_multiroot_fdfsolver_type * T
          = gsl_multiroot_fdfsolver_newton;
      gsl_multiroot_fdfsolver * s =
          gsl_multiroot_fdfsolver_alloc (T, 2);

  If there is insufficient memory to create the solver then the function returns a null pointer and the error handler is invoked with an error code of `GSL_ENOMEM`.

Function: int gsl_multiroot_fsolver_set (gsl_multiroot_fsolver * s, gsl_multiroot_function * f, const gsl_vector * x)
Function: int gsl_multiroot_fdfsolver_set (gsl_multiroot_fdfsolver * s, gsl_multiroot_function_fdf * fdf, const gsl_vector * x)

  These functions set, or reset, an existing solver s to use the function f or function and derivative fdf, and the initial guess x. Note that the initial position is copied from x, this argument is not modified by subsequent iterations.

Function: void gsl_multiroot_fsolver_free (gsl_multiroot_fsolver * s)
Function: void gsl_multiroot_fdfsolver_free (gsl_multiroot_fdfsolver * s)

  These functions free all the memory associated with the solver s.

Function: const char * gsl_multiroot_fsolver_name (const gsl_multiroot_fsolver * s)
Function: const char * gsl_multiroot_fdfsolver_name (const gsl_multiroot_fdfsolver * s)

  These functions return a pointer to the name of the solver. For example,

      printf ("s is a '%s' solver\n",
              gsl_multiroot_fdfsolver_name (s));

  would print something like `s is a 'newton' solver`.