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<h1>GNU Scientific Library for Lisp</h1>
<h2><a href="index.html">GSLL</a>
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<li><a href="#about">About</a></li>
<li><a href="#examples">Examples</a></li>
<li><a href="#require">Requirements</a></li>
<li><a href="#getit">Download</a></li>
<li><a href="#documentation">Documentation</a></li>
<li><a href="#status">Status</a></li>
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<h2>About</h2>
<a name="about"/>
<p class="first">
<p>The GNU Scientific Library for Lisp (GSLL) allows you to use
the <a href="http://www.gnu.org/software/gsl/">GNU Scientific Library
(GSL)</a> from <a href="http://www.lisp.org">Common Lisp</a>. 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.
</p>
<p>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
<a href="missing-features.text">missing-features.text</a>
on the status of some incomplete topics.
<p>The <a href="http://www.gnu.org/software/gsl/manual/html_node/Elliptic-Functions-_0028Jacobi_0029.html">Jacobian elliptic functions</a> <i>sn</i>, <i>cn</i>, and
<i>dn</i> are special functions (Chapter 7):</p>
<pre>
(jacobian-elliptic-functions 0.2d0 0.81d0)
0.19762082367187703d0
0.9802785369736752d0
0.9840560289645665d0
1.828927267118668d-318
1.4821969375237396d-321
2.023692885365746d-320
</pre>
<p>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 <i>m</i> is not greater than 1,
so an error is signalled if this parameter is out of range:
<pre>
(jacobian-elliptic-functions 0.61802d0 1.5d0)
Input domain error |m| > 1.0 in elljac.c at line 46
[Condition of type INPUT-DOMAIN]
<p>This is an ordinary Lisp error which may be handled with standard
definitions available in Lisp. To take the
<a href="file:///usr/share/doc/gsl-ref-html/Level-1-GSL-BLAS-Interface.html">
complex conjugate scalar product</a> of two complex vectors of length 3:
<pre>
(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)
</pre>
<p>or equivalently the vector arguments may be specified with reals,
<pre>
(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)
</pre>
<p>There are over 1200 examples available from within GSLL with the
function <code>examples</code>. These examples also serve
as a test suite for GSLL.
<h2>Requirements</h2>
<a name="require"/>
<p>
GSLL should work in any Common Lisp implementation and platform
combination for which the following are supported:</p>
<ul>
<li><a href="http://www.gnu.org/software/gsl/">GSL</a>
</li>
<li><a href="http://common-lisp.net/project/cffi/">CFFI</a>,
version 0.10.0 or newer; callbacks and <code>foreign-funcall</code> must be supported
</li>
<li><a href="http://www.cliki.net/trivial-garbage">trivial-garbage</a>
<li><a href="http://common-lisp.net/project/cl-utilities/">cl-utilities</a>
<li><a href="http://www.cliki.net/asdf">ASDF</a></li></ul>
<p>GSLL has been tested with
<a href="http://sbcl.sourceforge.net/">SBCL</a>
and
<a href="http://trac.clozure.com/openmcl">CCL</a>
on Debian amd64, and
<a href="http://sbcl.sourceforge.net/">SBCL</a>
and
<a href="http://clisp.cons.org/">CLISP</a> on Debian i386. There
are some known failures; see <a href="status.text">status.text</a>.
<h3>With <a href="http://git.or.cz">git</a> and asdf</h3>
<p>Download/update:
<ul>
<li><code>git clone git://repo.or.cz/gsll.git</code></li>
<li><code>git pull</code> in the <code>gsll</code> directory
afterwards to update</li>
</ul>
<p>The <a href="http://repo.or.cz/w/gsll.git"> repository web page</a>
can be used to browse or retrieve a compressed tarball (click the most
recent "snapshot" link).
You will need to make a link of <code>gsll.asd</code> and
optionally <code>gsll-tests.asd</code> to some directory known to ASDF.
Then in Lisp, load the system:
<ul>
<li><code>(asdf:operate 'asdf:load-op :gsll)</code></li>
</ul>
<h3>With <a href="http://common-lisp.net/project/clbuild/">clbuild</a></h3>
<p>
Add the following to <code>wnpp-projects</code>:
<ul>
<li><code>gsll get_git git://repo.or.cz/gsll.git</code></li>
<li><code>trivial-garbage get_darcs http://common-lisp.net/~loliveira/darcs/trivial-garbage</code></li>
<li><code>cl-utilities get_cvs_clnet</code></li>
<li><code>gsll cffi trivial-garbage cl-utilities</code></li>
</ul>
<p>
to <code>dependencies</code> and execute
from within the clbuild directory:
<ul>
<li><code>sudo ./clbuild update gsll</code></li>
</ul>
<h3>With Debian or Ubuntu</h3>
<ul>
<li><code>sudo aptitude install libgsl0-dev cl-cffi cl-utilities</code></li>
<li><code>git clone git://repo.or.cz/gsll.git</code></li>
<li><code>darcs get http://common-lisp.net/~loliveira/darcs/trivial-garbage</code></li>
<li><code>clc-register-user-package trivial-garbage/trivial-garbage.asd</code></li>
<li><code>clc-register-user-package gsll/gsll.asd</code></li>
<li><code>clc-register-user-package gsll/gsll-tests.asd</code></li>
</ul>
<p>
After starting your Lisp implementation,
<ul>
<li><code>(clc:clc-require :gsll)</code></li>
</ul>
<h3>Test suite</h3>
<p>The test suite may be run with
<ul>
<li><code>(asdf:operate 'asdf:load-op :gsll-tests)</code></li>
<li><code>(in-package :gsl)</code></li>
<li><code>(lisp-unit:run-tests)</code></li>
</ul>
<p>Please see <a href="status.text">status.text</a> for known failures.
<p>
This software is distributed under
the <a href="http://www.cliki.net/LLGPL">LLGPL</a>
and <a href="http://www.gnu.org/copyleft/fdl.html">FDL</a>; see
the file COPYING. There is absolutely no warranty.</p>
<h2>Documentation</h2>
<a name="documentation"/>
<h3>General Advice</h3>
<p>The following techniques for using the API are advised:</p>
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<li>Find the appropriate function(s) in the <a
href="http://www.gnu.org/software/gsl/manual/">GSL
documentation</a>.</li>
<li>Use the GSLL function <code>gsl-lookup</code>
to find the equivalent GSLL function, for example
<pre>
(gsl-lookup "gsl_sf_elljac_e")
JACOBIAN-ELLIPTIC-FUNCTIONS
T
</pre>
<p>
to find that the Lisp function name is <code>#'jacobian-elliptic-functions</code>.
</li>
<li>Look at the documentation for that Lisp function, e.g.
<pre>(documentation #'jacobian-elliptic-functions 'function)
"The Jacobian elliptic functions sn(u|m),
cn(u|m), dn(u|m) computed by descending Landen transformations."
</pre>
<p>
to get an explanation of the arguments etc.
</li>
<li>Use the function <code>(examples)</code> 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
<code>(examples 'higher-moments)</code>. The result will be a list
of forms, each providing an example of usage in the relevant topic.
If the
<a href="http://www.gnu.org/software/gsl/manual/">GSL
documentation</a> provides an example, there will usually be the same
or similar example provided in GSLL. <i>Note:</i> Some of the
examples are intentionally designed to signal an error, because the
examples also serve as a regression (unit) test suite for GSLL.</li>
Some examples are not yet present in, or are too complicated for, the
function <code>#'examples</code>. 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).
<h3>Arrays</h3>
<p>
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 <code>*array-element-types*</code>. 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.</p>
<p>
Common Lisp arrays should be created with <code>make-marray</code> or
<code>#m</code>:
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
Classes of vectors and matrices are named by appending the element
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type as hypenated words to "vector" or "matrix". The following table
shows the classes available on a 64-bit platform:
<center>
<table border=5 frame=all cellpadding=4 cellspacing=4 cols=6>
<caption align=top>Element types, vector and matrix
classes</caption>
<thead>
<tr><th><b>Element type</b><td><b>Vector class name</b>
<td><b>Matrix class name</b><td><b>#m prefix</b></thead>
<tbody>
<tr><td>double-float<td>vector-double-float<td>matrix-double-float
<td>1 or empty
<tr><td>(complex double-float)<td>vector-complex-double-float<td>matrix-complex-double-float<td>2
<tr><td>single-float<td>vector-single-float<td>matrix-single-float<td>3
<tr><td>(complex single-float)<td>vector-complex-single-float<td>matrix-complex-single-float<td>4
<tr><td>(signed-byte 8)<td>vector-signed-byte-8<td>matrix-signed-byte-8<td>7
<tr><td>(unsigned-byte 8)<td>vector-unsigned-byte-8<td>matrix-unsigned-byte-8<td>8
<tr><td>(signed-byte 16)<td>vector-signed-byte-16<td>matrix-signed-byte-16<td>15
<tr><td>(unsigned-byte 16)<td>vector-unsigned-byte-16<td>matrix-unsigned-byte-16<td>16
<tr><td>(signed-byte 32)<td>vector-signed-byte-32<td>matrix-signed-byte-32<td>31
<tr><td>(unsigned-byte 32)<td>vector-unsigned-byte-32<td>matrix-unsigned-byte-32<td>32
<tr><td>(signed-byte 64)<td>vector-signed-byte-64<td>matrix-signed-byte-64<td>63
<tr><td>(unsigned-byte 64)<td>vector-unsigned-byte-64<td>matrix-unsigned-byte-64<td>64
</tbody>
</table>
</center>
<p>
Individual elements are obtained using <code>maref</code> (analogous
to Lisp's <code>aref</code>), and are set
with <code>setf maref</code>. A complete CL array may
be extracted with the function <code>#'cl-array</code>.
</p>
<h3>GSL objects</h3>
<p>
There are a number of GSL objects other than arrays that can be
created:
<pre>
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
An instance may be created with a function whose name is "make-"
followed by the class name, e.g. <code>make-histogram</code>. The
arguments that the function takes depends on the class.
</p>
<h3>Additional definitions</h3>
<p>
Some definitions are provided because of their usefulness, even though
GSL doesn't have them.
<ul>
<li><code>invert-matrix</code> finds the inverse of a matrix and uses
GSL's LU decomposition functions.</li>
<li>IEEE floating point number analysis.</li>
</ul>
<h2>Status</h2>
<a name="status"/>
<p>
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
<a href="missing-features.text">missing-features.text</a>
for more details. Known bugs are documented in
<a href="status.text">status.text</a>. 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.
<h2>Contact</h2>
<a name="contact"/>
<p>There is a <a
href="http://common-lisp.net/cgi-bin/mailman/listinfo/gsll-devel">mailing
list</a> for all aspects of this project, including bug reports. In
addition, I am frequently on #lisp IRC channel as LiamH.
</p>
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<address><a href="mailto:gsll-devel@common-lisp.net">Liam Healy</a></address>
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