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GSL.jl

Julia wrapper for the GNU Scientific Library (GSL), for Julia v1.0+. Currently uses GSL v2.7.

Structure

The library tries to provide Julia interfaces to all the functions, types and symbols defined in the GSL documentation.

• Functions are interfaced without the gsl_ prefix, e.g. sf_legendre_Pl and vector_alloc.
• Types, global variables and most constants are interfaced using their original GSL name, e.g. gsl_vector, gsl_root_fdfsolver_newton and GSL_SUCCESS.
• The physical constants GSL_CONST_* can be found under the namespace GSL.Const, e.g. GSL.Const.MKSA_ANGSTROM.

Some functions have a secondary wrapper on top of the GSL interface, to make Julia usage more convenient, for example by allocating the output array. The low-level C interface to GSL can still be accessed under the namespace GSL.C. Some examples of functions that are different in the low-level interface:

GSL.strerror(gsl_errno) -> String
GSL.C.strerror(gsl_errno) -> Ptr{Cchar}
and
GSL.sf_legendre_array(norm, lmax, x) -> Array{Float64}
GSL.C.sf_legendre_array(norm, lmax, x, result_array) -> Cint

Parts of GSL are not interfaced to, since they provide functionality already existing in Julia. These are functions with prefixes gsl_spmatrix_, gsl_splinalg_, gsl_spblas_, gsl_eigen_, gsl_sort, gsl_blas_, cblas_, gsl_fft_, and gsl_linalg_. In addition, interfaces to gsl_bst_ functions are currently missing.

Examples

See examples in examples/ and tests test/ for more examples.

Special function with result struct

# Direct call
sf_legendre_P3(0.5)
# Output: -0.4375

# With result struct that stores value and error:
sf_legendre_P3_e(0.5)
# Output: gsl_sf_result_struct(-0.4375, 3.3306690738754696e-16)

# Low-level call with result struct as argument:
result = gsl_sf_result(0,0)
GSL.C.sf_legendre_P3_e(0.5, result)
# Output: GSL_SUCCESS
# result = gsl_sf_result_struct(-0.4375, 3.3306690738754696e-16)

Special function with array output

x = 0.5
lmax = 4
result = sf_legendre_array(GSL_SF_LEGENDRE_SPHARM, lmax, x)
# Equivalent using low-level interface:
n = sf_legendre_array_n(lmax)
result = Array{Float64}(undef, n)
GSL.C.sf_legendre_array(GSL_SF_LEGENDRE_SPHARM, lmax, x, result)

Root finding

f = x -> x^5+1
df = x -> 5*x^4
fdf = @gsl_function_fdf(f, df)
solver = root_fdfsolver_alloc(gsl_root_fdfsolver_newton)
root_fdfsolver_set(solver, fdf, -2)
while abs(f(root_fdfsolver_root(solver))) > 1e-10
    root_fdfsolver_iterate(solver)
end
println("x = ", root_fdfsolver_root(solver))
# Output: x = -1.0000000000104232

Documentation

Extra functionality defined in this package:

• Convenice functions hypergeom and hypergeom_e for the hypergeometric functions.
• Function wrapping macros @gsl_function, @gsl_function_fdf, @gsl_multiroot_function and @gsl_multiroot_function_fdf that are used for packaging Julia functions so that they can be passed to GSL.
• Functions wrap_gsl_vector and wrap_gsl_matrix that return a Julia array or matrix pointing to the data in a gsl_vector or gsl_matrix.

In addition, some effort has been put into giving most types and functions proper docstrings, e.g.

help?> GSL.wavelet_free
  wavelet_free(w) -> Cvoid

  C signature: void gsl_wavelet_free (gsl_wavelet * w)

  GSL documentation:

  void gsl_wavelet_free (gsl_wavelet * w)
  –––––––––––––––––––––––––––––––––––––––––

  │  This function frees the wavelet object w.

help?> GSL.gsl_wavelet
  mutable struct gsl_wavelet
      type::Ptr{gsl_wavelet_type}
      h1::Ptr{Cdouble}
      g1::Ptr{Cdouble}
      h2::Ptr{Cdouble}
      g2::Ptr{Cdouble}
      nc::Csize_t
      offset::Csize_t
  end

  GSL documentation:

  gsl_wavelet
  –––––––––––––

  │  This structure contains the filter coefficients defining the wavelet and any associated offset parameters.

Behind the scenes

• All interface code in src/gen is created by running the script gen/makewrappers.jl, which attempts to parse the GSL headers using regular expressions.
• Heuristics for creating convenience functions are in gen/heuristic.jl.
• Docstrings are created from the GSL docs in gen/readdocs.jl.
• Hand-written convenience functions are in src/manual_wrappers.jl.