[OBSOLETE]
GNU Scientific Library for Lisp
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 Lispnatural 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, quasirandom sequences, random distributions, statistics, histograms, Ntuples, Monte Carlo integration, simulated annealing, ordinary differential equations, interpolation, numerical integration, numerical differentiation, Chebyshev approximation, series acceleration, discrete Hankel transforms, rootfinding, minimization, leastsquares fitting, IEEE floatingpoint, discrete wavelet transforms, basis splines, physical constants. See missingfeatures.text on the status of some incomplete topics.
Examples
The Jacobian elliptic functions sn, cn, and dn are special functions (Chapter 7):
(jacobianellipticfunctions 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:
(jacobianellipticfunctions 0.61802d0 1.5d0)
Input domain error m > 1.0 in elljac.c at line 46
[Condition of type INPUTDOMAIN]
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 libgsl0dev
and libffidev
. Once they are installed and you have loaded the quicklisp file:
(ql:quickload "gsll")
To test your installation:
(asdf:testsystem :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
gsllookup
to find the equivalent GSLL function, for example(gsllookup "gsl_sf_elljac_e") JACOBIANELLIPTICFUNCTIONS T
to find that the Lisp function name is
#'jacobianellipticfunctions
. 
Look at the documentation for that Lisp function, e.g.
(documentation #'jacobianellipticfunctions 'function) "The Jacobian elliptic functions sn(um), cn(um), dn(um) 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 'highermoments)
. 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 (onedimensional arrays) and matrices (twodimensional arrays). Foreign arrays are defined and manipulated using the Antik which defines generic operations on arraylike 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:*arrayelementtypes*
.
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 levintruncated spline
nonlinearffit nonlinearfdffit
onedimensionalrootsolverf onedimensionalrootsolverfdf
multidimensionalminimizerf multidimensionalminimizerfdf
fitworkspace onedimensionalminimizer
multidimensionalrootsolverf multidimensionalrootsolverfdf
histogram histogram2d histogrampdf histogram2dpdf
basisspline chebyshev hankel wavelet waveletworkspace
randomnumbergenerator quasirandomnumbergenerator discreterandom
polynomialcomplexworkspace integrationworkspace
qawstable qawotable
eigensymm eigensymmv eigenherm eigenhermv
eigennonsymm eigennonsymmv eigengensymm eigengensymmv
eigengen eigengenv
montecarloplain montecarlomiser montecarlovegas
odestepper odeevolution standardcontrol ycontrol
ypcontrol scaledcontrol
fftrealwavetabledoublefloat fftrealwavetablesinglefloat
fftrealworkspacedoublefloat fftrealworkspacesinglefloat
fftcomplexwavetabledoublefloat fftcomplexwavetablesinglefloat
fftcomplexworkspacedoublefloat fftcomplexworkspacesinglefloat
ffthalfcomplexwavetabledoublefloat ffthalfcomplexwavetablesinglefloat
An instance may be created with a function whose name is "make" followed by the class name, e.g. makehistogram
. 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.

invertmatrix
finds the inverse of a matrix and uses GSL's LU decomposition functions.  IEEE floating point number analysis.

fftfrequencyvector
returns a vector where the sample frequencies are contained. If you perform an FFT on a vector of a given size and :samplesize, this vector will contain the sample frequencies in order. If the :shifted keyword is T, then the frequencies are ordered in ascending order. 
fftshift
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. 
fftinverseshift
performs the inverse action of fftshift; 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 missingfeatures.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 formatpatch origin
This will produce one or more files whose names start with a fourdigit number; please attach them all to your email.
Liam Healy Timestamp: