## 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, fast Fourier transforms (FFT), quadrature, random numbers, quasi-random sequences, random distributions, statistics, histograms, N-tuples, Monte Carlo integration, simulated annealing, 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, physical constants. 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

which returns as multiple values the three function values. 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)

There are over 1500 examples available from within GSLL with the
function `examples`

. There is also a suite of over
4000 tests; many of the examples also serve as tests, and most others
are ported from GSL's tests.

## Download and Install

### Download

Use quicklisp and follow the
instructions. You will need to make sure that the libraries and
header files associated with GNU Scientific Library
(GSL) and libffi are
installed; your distribution may name these `libgsl0-dev`

and `libffi-dev`

. Once they are installed and you have
loaded the quicklisp file:

(ql:quickload "gsll")

To test your installation:

(asdf:test-system :gsll)

The result should look something like:

Unit Test Summary | 3997 assertions total | 3992 passed | 5 failed | 6 execution errors | 0 missing tests

You may see more failures; if you are not on a 64 bit platform you will see fewer assertions.

### License

This software is distributed under the GPL ; see the file COPYING. There is absolutely no warranty.

## Documentation

### General Advice

The following techniques for using the API are advised:

- Find the appropriate function(s) in the GSL documentation.
- Use the GSLL function
`gsl-lookup`

to find the equivalent GSLL function, for example(gsl-lookup "gsl_sf_elljac_e") JACOBIAN-ELLIPTIC-FUNCTIONS T

to find that the Lisp function name is

`#'jacobian-elliptic-functions`

. - Look at the documentation for that Lisp function, e.g.
(documentation #'jacobian-elliptic-functions 'function) "The Jacobian elliptic functions sn(u|m), cn(u|m), dn(u|m) computed by descending Landen transformations."

to get an explanation of the arguments etc.

- Use the function
`(examples)`

without an argument to get a list of example categories. Then use the function with a category name as the argument to get a list of examples under that category, for example`(examples 'higher-moments)`

. The result will be a list of forms, each providing an example of usage in the relevant topic. If the GSL documentation provides an example, there will usually be the same or similar example provided in GSLL.*Note:*Some of the examples are intentionally designed to signal an error, because the examples also serve as a regression (unit) test suite for GSLL.

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). Foreign arrays are defined and
manipulated using
the Antik
which defines generic operations on array-like objects; see the Antik
documentation for more information. 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 `grid:*array-element-types*`

.

### Passing functions

Functions that are passed to GSL functions (known as *callbacks*
in C) are specified with a
function
designator for the CL function, that is, either the function
object itself or a symbol denoting the function.
There is usually an option `scalarsp`

for functions
that take or return arrays that, if true, will
send the user function the argument element by element, and expect
the return values to be the individual elements.

### 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 qaws-table qawo-table eigen-symm eigen-symmv eigen-herm eigen-hermv eigen-nonsymm eigen-nonsymmv eigen-gensymm eigen-gensymmv eigen-gen eigen-genv monte-carlo-plain monte-carlo-miser monte-carlo-vegas ode-stepper ode-evolution standard-control y-control yp-control scaled-control fft-real-wavetable-double-float fft-real-wavetable-single-float fft-real-workspace-double-float fft-real-workspace-single-float fft-complex-wavetable-double-float fft-complex-wavetable-single-float fft-complex-workspace-double-float fft-complex-workspace-single-float fft-half-complex-wavetable-double-float fft-half-complex-wavetable-single-float

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.

`invert-matrix`

finds the inverse of a matrix and uses GSL's LU decomposition functions.- IEEE floating point number analysis.
`fft-frequency-vector`

returns a vector where the sample frequencies are contained. If you perform an FFT on a vector of a given size and :sample-size, this vector will contain the sample frequencies in order. If the :shifted keyword is T, then the frequencies are ordered in ascending order.`fft-shift`

returns a copy of a vector where the zero frequency has been shifted to the center; the frequency components will be sorted according to their frequency, in ascending order. Optionally, a :stride can be provided.`fft-inverse-shift`

performs the inverse action of fft-shift; the zero and positive frequency components are shifted to the beginning, so that the resulting vector is suitable for an inverse FFT. Optionally, a :stride can be provided.

## Status

GSLL is largely complete and usable, with functioning interfaces to most of GSL. Some functionality is not yet ported; 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. See also the archives. In addition, I am frequently on #lisp IRC channel as LiamH. For bug reports, please use the mailing list. The development site for GSLL has the git repository. If you have patch(es), please commit your changes and do:

git format-patch origin

This will produce one or more files whose names start with a four-digit number; please attach them all to your email.