About

The GNU Scientific Library for Lisp (GSLL) allows you to use the GNU Scientific Library (GSL) from Common Lisp. This library provides a full range of common mathematical operations useful to scientific and engineering applications. The design of the GSLL interface is such that access to most of the GSL library is possible in a Lisp-natural way; the intent is that the user not be hampered by the restrictions of the C language in which GSL has been written. GSLL thus provides interactive use of GSL for getting quick answers, even for someone not intending to program in Lisp.

Topics include: polynomials, special functions, vectors and matrices, permutations, sorting, linear algebra including BLAS, eigensystems, quadrature, random numbers, quasi-random sequences, random distributions, statistics, histograms, N-tuples, Monte Carlo integration, ordinary differential equations, interpolation, numerical integration, numerical differentiation, Chebyshev approximation, series acceleration, discrete Hankel transforms, root-finding, minimization, least-squares fitting, IEEE floating-point, discrete wavelet transforms, basis splines. See missing-features.text on the status of some incomplete topics.

Examples

The Jacobian elliptic functions sn, cn, and dn are special functions (Chapter 7):

(jacobian-elliptic-functions 0.2d0 0.81d0)
0.19762082367187703d0
0.9802785369736752d0
0.9840560289645665d0
1.828927267118668d-318
1.4821969375237396d-321
2.023692885365746d-320

which returns as multiple values the three function values, along with the estimated errors of each. The functions are defined only if the second argument m is not greater than 1, so an error is signalled if this parameter is out of range:

(jacobian-elliptic-functions 0.61802d0 1.5d0)
Input domain error |m| > 1.0 in elljac.c at line 46
   [Condition of type INPUT-DOMAIN]

This is an ordinary Lisp error which may be handled with standard definitions available in Lisp. To take the complex conjugate scalar product of two complex vectors of length 3:

(cdot #2m(#c(-34.5d0 8.24d0) #c(3.29d0 -8.93d0) #c(34.12d0 -6.15d0))
      #2m(#c(49.27d0 -13.49d0) #c(32.5d0 42.73d0) #c(-17.24d0 43.31d0)))
#C(-2940.2118d0 1861.9380999999998d0)

or equivalently the vector arguments may be specified with reals,

(cdot #2m(-34.5d0 8.24d0 3.29d0 -8.93d0 34.12d0 -6.15d0)
      #2m(49.27d0 -13.49d0 32.5d0 42.73d0 -17.24d0 43.31d0))
#C(-2940.2118d0 1861.9380999999998d0)

There are over 1200 examples available from within GSLL with the function examples. These examples also serve as a test suite for GSLL.

Requirements

GSLL should work in any Common Lisp implementation and platform combination for which the following are supported:

GSLL has been tested with SBCL and CCL on Debian amd64, and SBCL and CLISP on Debian i386. There are some known failures; see status.text.

Download and Install

With git and asdf

Download/update:

The repository web page can be used to browse or retrieve a compressed tarball (click the most recent "snapshot" link). You will need to make a link of gsll.asd and optionally gsll-tests.asd to some directory known to ASDF. Then in Lisp, load the system:

With clbuild

Add the following to wnpp-projects:

and add

to dependencies and execute from within the clbuild directory:

With Debian or Ubuntu

After starting your Lisp implementation,

Test suite

The test suite may be run with

Please see status.text for known failures.

License

This software is distributed under the LLGPL and FDL; see the file COPYING. There is absolutely no warranty.

Documentation

General Advice

The following techniques for using the API are advised:

Some examples are not yet present in, or are too complicated for, the function #'examples. In this case, you need to look in the relevant source file; they are in either a separate file of examples, or at the end of the file of definitions. It is advisable to look at the examples first for calculations that require more complex setup (generally, the later chapters in the GSL manual).

Arrays

GSLL has many functions that work on vectors (one-dimensional arrays) and matrices (two-dimensional arrays). GSLL supports all array element types that are supported by CFFI, the CL implementation, GSL, and the platform. This list is available in the variable *array-element-types*. On implementations that support it (currently only SBCL), the contents are directly available to the GSL functions without copying between the Lisp area and the C area of memory.

Common Lisp arrays should be created with make-marray or #m: The #m reader macro in the default form creates a vector or matrix of element type double-float, which is the most common type needed for GSL functions. It optionally takes a numeric argument prefix as in the example above to make an array with a different element type; a guide to the numeric argument is given below. If the macro is followed by a list of numbers, a vector is created, if it is followed by a list of lists of numbers, each of the same length, a matrix is created.

Classes of vectors and matrices are named by appending the element type as hypenated words to "vector" or "matrix". The following table shows the classes available on a 64-bit platform:

Element types, vector and matrix classes
Element typeVector class name Matrix class name#m prefix
double-floatvector-double-floatmatrix-double-float 1 or empty
(complex double-float)vector-complex-double-floatmatrix-complex-double-float2
single-floatvector-single-floatmatrix-single-float3
(complex single-float)vector-complex-single-floatmatrix-complex-single-float4
(signed-byte 8)vector-signed-byte-8matrix-signed-byte-87
(unsigned-byte 8)vector-unsigned-byte-8matrix-unsigned-byte-88
(signed-byte 16)vector-signed-byte-16matrix-signed-byte-1615
(unsigned-byte 16)vector-unsigned-byte-16matrix-unsigned-byte-1616
(signed-byte 32)vector-signed-byte-32matrix-signed-byte-3231
(unsigned-byte 32)vector-unsigned-byte-32matrix-unsigned-byte-3232
(signed-byte 64)vector-signed-byte-64matrix-signed-byte-6463
(unsigned-byte 64)vector-unsigned-byte-64matrix-unsigned-byte-6464

Individual elements are obtained using maref (analogous to Lisp's aref), and are set with setf maref. A complete CL array may be extracted with the function #'cl-array.

Passing functions

Functions that are passed to GSL functions (known as callbacks in C) are defined with one of the following macros in GSLL, depending on the application:

The function may be specified as the name of a CL function, or as a lambda form. If the latter, the dimensions need not be specified in make-single-function, make-monte-carlo-function, or make-solver-functions for derivative-free solvers; they will be computed from the arglist. Each of these macros will return a foreign pointer that can be passed to the appropriate GSL function that requires a function.

GSL objects

There are a number of GSL objects other than arrays that can be created:

acceleration interpolation levin levin-truncated spline
nonlinear-ffit nonlinear-fdffit
one-dimensional-root-solver-f one-dimensional-root-solver-fdf
multi-dimensional-minimizer-f multi-dimensional-minimizer-fdf
fit-workspace one-dimensional-minimizer
multi-dimensional-root-solver-f multi-dimensional-root-solver-fdf
histogram histogram2d histogram-pdf histogram2d-pdf
basis-spline chebyshev hankel wavelet wavelet-workspace
random-number-generator quasi-random-number-generator discrete-random
polynomial-complex-workspace integration-workspace
eigen-symm eigen-symmv eigen-herm eigen-hermv
monte-carlo-plain monte-carlo-miser monte-carlo-vegas
ode-stepper ode-evolution standard-control y-control
yp-control scaled-control

An instance may be created with a function whose name is "make-" followed by the class name, e.g. make-histogram. The arguments that the function takes depends on the class.

Additional definitions

Some definitions are provided because of their usefulness, even though GSL doesn't have them.

Status

GSLL is largely complete and usable, with functioning interfaces to most of GSL. Some functionality is not yet ported, particularly those introduced in the more recent versions of GSL; see missing-features.text for more details. Known bugs are documented in status.text. Work is ongoing to both remedy those deficiencies and to simplify the user interface by changing more required arguments into optional or key arguments with useful default values. Typically, these arguments bind GSL objects and arrays used internally or for function return.

Contact

There is a mailing list for all aspects of this project, including bug reports. In addition, I am frequently on #lisp IRC channel as LiamH.