1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html>
<HEAD>
<TITLE>Using lpsolve from R</TITLE>
<style TYPE="text/css"> BODY { font-family:verdana,arial,helvetica; margin:15; }
</style>
</HEAD>
<BODY>
<h1 align="left"><u>Using lpsolve from R</u></h1>
<a name="R"></a>
<h3>R?</h3>
<P> R is a language and environment for
statistical computing and graphics. It is a <a
href="http://www.gnu.org" target="_top">GNU
project</a> which is similar to the S language and environment which
was developed at Bell Laboratories (formerly AT&T, now Lucent
Technologies) by John Chambers and colleagues. R can be considered as
a different implementation of S. There are some important differences,
but much code written for S runs unaltered under R.
</P>
<P>
R provides a wide variety of statistical (linear and nonlinear
modelling, classical statistical tests, time-series analysis,
classification, clustering, ...) and graphical techniques, and is
highly extensible. The S language is often the vehicle of choice for
research in statistical methodology, and R provides an Open Source
route to participation in that activity.
</P>
<P>
One of R's strengths is the ease with which well-designed
publication-quality plots can be produced, including mathematical
symbols and formulae where needed. Great care has been taken over the
defaults for the minor design choices in graphics, but the user
retains full control.
</P>
<p>R is available as Free Software under the terms of the <a
href="http://www.gnu.org" target="_top">Free Software Foundation</a>'s
GNU General Public License in source code
form. It compiles and runs on a wide variety of UNIX platforms and
similar systems (including FreeBSD and Linux), Windows and MacOS.
</P>
<H2>The R environment</H2>
<P>
R is an integrated suite of software facilities for data
manipulation, calculation and graphical display. It includes
</P>
<UL>
<LI>an effective data handling and storage facility,
<LI>a suite of operators for calculations on arrays, in particular matrices,
<LI>a large, coherent, integrated collection of intermediate tools for data
analysis,
<LI>graphical facilities for data analysis and display either
on-screen or on hardcopy, and
<LI>a well-developed, simple and effective programming language which
includes conditionals, loops, user-defined recursive functions and
input and output facilities.
</UL>
<P>
The term "environment" is intended to characterize it as a fully
planned and coherent system, rather than an incremental accretion of
very specific and inflexible tools, as is frequently the case with other
data analysis software.
</P>
<P>
R, like S, is designed around a true computer language, and it allows
users to add additional functionality by defining new functions. Much
of the system is itself written in the R dialect of S, which makes it
easy for users to follow the algorithmic choices made. For
computationally-intensive tasks, C, C++ and Fortran code can be linked
and called at run time. Advanced users can write C code to manipulate
R objects directly.
</P>
<P>
Many users think of R as a statistics system. We prefer to think of
it of an environment within which statistical techniques are
implemented. R can be extended (easily) via <EM>packages</EM>. There
are about eight packages supplied with the R distribution and many
more are available through the CRAN family of Internet sites covering
a very wide range of modern statistics.
</P>
<p>We will not discuss the specifics of R here but instead refer the reader to the
<a href="http://www.r-project.org/">R</a> website. Also see <a href="http://cran.r-project.org/doc/manuals/R-intro.html">An Introduction to R</a>
</p>
<a name="R_and_lpsolve"></a>
<h3>R and lpsolve</h3>
<p>lpsolve is callable from R via an extension or module. As such, it looks like lpsolve is fully integrated
with R. Matrices can directly be transferred between R and lpsolve in both directions. The complete interface
is written in C so it has maximum performance.
</p>
<p>There are currently two R packages based on lp_solve. Both packages are available from <a href="http://cran.r-project.org/">CRAN</a>.
</p>
<p>
The <i>lpSolve</i> R package is the first implementation of an interface of lpsolve to R.
It provides high-level functions for solving general linear/integer problems, assignment problems and transportation problems.
The following link contains the version of the driver: <a href="http://cran.r-project.org/web/packages/lpSolve/index.html">lpSolve: Interface to Lp_solve v. 5.5 to solve linear/integer programs</a>.
It does not contain the lpsolve API. Only the higher level calls.
Documentation for this interface can be found on: <a href="http://rweb.stat.umn.edu/R/library/lpSolve/html/00Index.html">Interface to Lp_solve v. 5.5 to solve linear/integer programs</a><br>
This driver is written and maintained by <a href="mailto:buttrey@nps.edu">Sam Buttrey</a>.
</p>
<p>The <i>lpSolveAPI</i> R package is a second implementation of an interface of lpsolve to R.
It provides an R API mirroring the lp_solve C API and hence provides a great deal more functionality but has a steeper learning curve.
The R interface to lpsolve contains its own documentation.
See <a href="http://lpsolve.r-forge.r-project.org/">An R interface to the lp_solve library</a> for the driver.<br>
This driver is written and maintained by <a href="mailto:kjell.konis@epfl.ch">Kjell Konis</a>.
</p>
<a name="Installing_the_lpsolve_driver_in_R"></a>
<h3>Installing the lpsolve driver in R</h3>
<p>How to install the driver depends on the environment.
</p>
<h5>Windows</h5>
<p>In the RGui menu, there is a menu item 'Packages'. From there a package can be installed from a CRAN mirror or from a local zip file.
</p>
<h5>R command line</h5>
<p>
Packages can also be installed from the R command line. This is a more general approach that will work under all environments.<br>
Installing the package takes a single command:
</p>
<p>
<!--
<pre>
> install.packages("lpSolve", repos = "http://r-forge.r-project.org")
</pre>
-->
The lpSolve R package:
</p>
<pre>
> install.packages("lpSolve")
</pre>
and to install the lpSolveAPI package use the command:
<pre>
> install.packages("lpSolveAPI")
</pre>
<h5>Note</h5>
<p>
The <tt>></tt> shown before each R command is the R prompt. Only the text after <tt>></tt> must be entered.
</p>
<a name="Loading_the_lpsolve_driver_in_R"></a>
<h3>Loading the lpsolve driver in R</h3>
Installing the package is not enough. It must also loaded in the R memory space before it can be used.
This can be done with the following command:
<pre>
> library(lpSolveAPI)
</pre>
Or
<pre>
> library("lpSolveAPI", character.only=TRUE)
</pre>
<h3>Getting Help</h3>
<p>
Documentation is provided for each function in the lpSolve package using R's built-in help system. For example, the command
</p>
<pre>
> ?add.constraint
</pre>
will display the documentation for the <tt>add.constraint</tt> function.
<h3>Building and Solving Linear Programs Using the lpSolve R Package</h3>
<p>
This implementation provides the functions <tt>lp</tt>, <tt>lp.assign</tt>, <tt>lp.object</tt>, <tt>lp.transport</tt> and <tt>print.lp</tt>. These functions allow a linear program (and transport and assignment problems) to be defined and solved using a single command.
</p>
<p>
For more information enter:
</p>
<pre>
> ?lp
</pre>
<pre>
> ?lp.assign
</pre>
<pre>
> ?lp.object
</pre>
<pre>
> ?lp.transport
</pre>
<pre>
> ?print.lp
</pre>
<p>See also <a href="http://rweb.stat.umn.edu/R/library/lpSolve/html/00Index.html">Interface to Lp_solve v. 5.5 to solve linear/integer programs</a>
</p>
<h3>Building and Solving Linear Programs Using the lpSolveAPI R Package</h3>
<p>
This implementation provides an API for building and solving linear programs that mimics the lp_solve C API. This approach allows much greater flexibility but also has a few caveats. The most important is that the <i>lpSolve linear program model objects</i> created by <tt>make.lp</tt> and <tt>read.lp</tt> are not actually R objects but external pointers to lp_solve 'lprec' structures. R does not know how to deal with these structures. In particular, R cannot duplicate them. Thus one must never assign an existing lpSolve linear program model object in R code.
</p>
<p>To load the library, enter:
</p>
<pre>
> library(lpSolveAPI)
</pre>
<p>
Consider the following example. First we create an empty model x.
</p>
<pre>
> x <- make.lp(2, 2)
</pre>
Then we assign x to y.
<pre>
> y <- x
</pre>
Next we set some columns in x.
<pre>
> set.column(x, 1, c(1, 2))
> set.column(x, 2, c(3, 4))
</pre>
<p>
And finally, take a look at y.
</p>
<pre>
> y
Model name:
C1 C2
Minimize 0 0
R1 1 3 free 0
R2 2 4 free 0
Type Real Real
upbo Inf Inf
lowbo 0 0
</pre>
The changes we made in x appear in y as well. Although x and y are two distinct objects in R, they both refer to the <b>same</b> lp_solve 'lprec' structure.
<p>
The safest way to use the lpSolve API is inside an R function - do not return the lpSolve linear program model object.
</p>
<h5>Learning by Example</h5>
<pre>
> lprec <- make.lp(0, 4)
> set.objfn(lprec, c(1, 3, 6.24, 0.1))
> add.constraint(lprec, c(0, 78.26, 0, 2.9), ">=", 92.3)
> add.constraint(lprec, c(0.24, 0, 11.31, 0), "<=", 14.8)
> add.constraint(lprec, c(12.68, 0, 0.08, 0.9), ">=", 4)
> set.bounds(lprec, lower = c(28.6, 18), columns = c(1, 4))
> set.bounds(lprec, upper = 48.98, columns = 4)
> RowNames <- c("THISROW", "THATROW", "LASTROW")
> ColNames <- c("COLONE", "COLTWO", "COLTHREE", "COLFOUR")
> dimnames(lprec) <- list(RowNames, ColNames)</pre>
Lets take a look at what we have done so far.
<pre>
> lprec # or equivalently print(lprec)
Model name:
COLONE COLTWO COLTHREE COLFOUR
Minimize 1 3 6.24 0.1
THISROW 0 78.26 0 2.9 >= 92.3
THATROW 0.24 0 11.31 0 <= 14.8
LASTROW 12.68 0 0.08 0.9 >= 4
Type Real Real Real Real
upbo Inf Inf Inf 48.98
lowbo 28.6 0 0 18
</pre>
Now lets solve the model.
<pre>
> solve(lprec)
[1] 0
> get.objective(lprec)
[1] 31.78276
> get.variables(lprec)
[1] 28.60000 0.00000 0.00000 31.82759
> get.constraints(lprec)
[1] 92.3000 6.8640 391.2928
</pre>
<p>
Note that there are some commands that return an answer. For the accessor functions (generally named get.*) the output should be clear. For other functions (e.g., <tt>solve</tt>), the interpretation of the returned value is described in the documentation. Since <tt>solve</tt> is generic in R, use the command
</p>
<pre>
> ?solve.lpExtPtr
</pre>
to view the appropriate documentation. The assignment functions (generally named set.*) also have a return value - often a logical value indicating whether the command was successful - that is returned invisibly. Invisible values can be assigned but are not echoed to the console. For example,
<pre>
> status <- add.constraint(lprec, c(12.68, 0, 0.08, 0.9), ">=", 4)
> status
[1] TRUE
</pre>
indicates that the operation was successful. Invisible values can also be used in flow control.
<h5>Cleaning up</h5>
<p>To free up resources and memory, the R command rm() must be used.<br>
For example:</p>
<pre>
> rm(lprec)
</pre>
<p>See also <a href="MATLAB.htm">Using lpsolve from MATLAB</a>,
<a href="O-Matrix.htm">Using lpsolve from O-Matrix</a>,
<a href="Sysquake.htm">Using lpsolve from Sysquake</a>,
<a href="Octave.htm">Using lpsolve from Octave</a>,
<a href="FreeMat.htm">Using lpsolve from FreeMat</a>,
<a href="Euler.htm">Using lpsolve from Euler</a>,
<a href="Python.htm">Using lpsolve from Python</a>,
<a href="Sage.htm">Using lpsolve from Sage</a>,
<a href="PHP.htm">Using lpsolve from PHP</a>,
<a href="Scilab.htm">Using lpsolve from Scilab</a>
<a href="MSF.htm">Using lpsolve from Microsoft Solver Foundation</a>
</p>
</BODY>
</html>
|