<!-- -*- mode: HTML; time-stamp-line-limit: -18; -*- --> <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"> <html> <head> <title>GSLL, the GNU Scientific Library for Lisp </title> <meta name="generator" content="muse.el"> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <link rev="made" href="mailto:lhealy@common-lisp.net"> <link rel="stylesheet" type="text/css" href="site.css"> </head> <body> <div id="banner"> <h1>GNU Scientific Library for Lisp</h1> <h2><a href="index.html">GSLL</a> </div> <div id="sidebar"> <ul> <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> <li><a href="#contact">Contact</a></li> </ul> <!-- Insertion Mark --> </div> <div id="content"> <!-- Page published by Emacs Muse begins here --> <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, fast Fourier transforms, 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 <a href="missing-features.text">missing-features.text</a> on the status of some incomplete topics. </p> <h2>Examples</h2> <a name="examples"/> <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] </pre> <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 1500 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> and cffi-grovel, version 0.10.5 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> <li><a href="http://www.cliki.net/asdf">ASDF</a></li> <li><a href="http://repo.or.cz/w/lisp-unit.git">lisp-unit</a>, <i>(Optional)</i> necessary to run <code>gsll-tests</code> </li> <li><a href="http://repo.or.cz/w/fsbv.git">FSBV</a>, <i>(Optional)</i> necessary for functions using complex scalars or simulated annealing </li> <li> <a href="http://common-lisp.net/project/iterate/">iterate</a> and <a href="http://common-lisp.net/project/asdf-system-connections/">asdf-system-connnections</a>, <i>(Optional)</i> provides a convenient way to iterate over elements or indices of vectors or matrices. </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>. </p> <h2>Download and Install</h2> <h3>With <a href="http://git.or.cz">git</a> and asdf</h3> <a name="getit"/> <p>Download/update: <ul> <li><code>git clone git://repo.or.cz/gsll.git</code></li> <li><code>git clone git://repo.or.cz/fsbv.git</code></li> <li><code>darcs get http://common-lisp.net/~loliveira/darcs/trivial-garbage</code></li> <li><code>git pull</code> in the <code>gsll</code> and <code>fsbv</code> directories 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> <p>If you wish to run the test suite, you must get lisp-unit and make it known to ASDF: <ul> <li><code>git clone git://repo.or.cz/lisp-unit.git</code></li> </ul> <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. <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>fsbv get_git git://repo.or.cz/fsbv.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> </ul> <p>and add <ul> <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 libffi-dev cl-iterate</code></li> <li><code>git clone git://repo.or.cz/gsll.git</code></li> <li><code>git clone git://repo.or.cz/fsbv.git</code></li> <li><code>darcs get http://common-lisp.net/~loliveira/darcs/trivial-garbage</code></li> <li><code>darcs get http://common-lisp.net/project/asdf-system-connections</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> <li><code>clc-register-user-package trivial-garbage/trivial-garbage.asd</code></li> <li><code>clc-register-user-package fsbv/fsbv.asd</code></li> <li><code>clc-register-user-package asdf-system-connections/asdf-system-connections.asd</li> </ul> <p> After starting your Lisp implementation, <ul> <li><code>(clc:clc-require :gsll-tests)</code></li> </ul> <h3>License</h3> <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> <ul> <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> </ul> <p> 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. It should be followed by a list; this list will be evaluated. If the list contains <code>^</code>, the object created will be a matrix and each row is ended with that symbol. <p> 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: <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> <p>Copying marrays is performed with the function <code>copy</code>. This works between marrays, pointers, and CL arrays. It is useful for functions intended to be passed to GSL functions (for e.g. solving, minimizing or fitting) that need to set a GSL vector or matrix, because one can simply copy into the passed-in pointer. </p> <p>There are two functions provided to extract the dimensions of a vector or array: <code>dim0</code> and <code>dim1</code>; the latter is applicable only for matrices. </p> <p>If you use <a href="http://common-lisp.net/project/iterate/">iterate</a>, there are extensions defined that make it easier to iterate over marrays. These are: <ul> <li><code>matrix-row</code>, <code>matrix-row-index</code></li> <li><code>matrix-column</code>, <code>matrix-column-index</code></li> <li><code>vector-element</code>, <code>vector-element-index</code></li> <li><code>matrix-element</code>, <code>matrix-element-index</code></li> </ul> <p>For example, <pre> (defparameter m1 #m(1 2 3 ^ 0 6 8)) (iter:iter (iter:for e :matrix-element m1) (princ e) (princ " ")) 1.0 2.0 3.0 0.0 0.0 6.0 8.0 </pre> <h3>Passing functions</h3> <p> Functions that are passed to GSL functions (known as <i>callbacks</i> in C) are specified with a <a href="http://www.lispworks.com/documentation/HyperSpec/Body/26_glo_f.htm#function_designator">function designator</a> for the CL function, that is, either the function object itself or a symbol denoting the function. There is usually an option <code>scalarsp</code> 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. </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 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 </pre> <p> 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; 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> </div> <!-- Page published by Emacs Muse ends here --> <div class="footer"> <hr> <address><a href="mailto:gsll-devel@common-lisp.net">Liam Healy</a></address> <!-- Created: Feb 25 2005 --> <!-- hhmts start --> <small> Time-stamp: <2009-10-28 22:49:53EDT index.html> </small> <!-- hhmts end --> </div> <script type="text/javascript"> var gaJsHost = (("https:" == document.location.protocol) ? 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