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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html>
<HEAD>
<TITLE>Using lpsolve from Python</TITLE>
<style TYPE="text/css"> BODY { font-family:verdana,arial,helvetica; margin:15; }
</style>
</HEAD>
<BODY>
<h1 align="left"><u>Using lpsolve from Python</u></h1>
<a name="Python"></a>
<h3>Python?</h3>
<p>Python is an <em>interpreted, interactive, object-oriented</em> programming
language. It is often compared to Tcl, Perl, Scheme or Java.</p>
<p>Python combines remarkable power with very clear syntax. It has
modules, classes, exceptions, very high level dynamic data types, and
dynamic typing. There are interfaces to many system calls and
libraries, as well as to various windowing systems (X11, Motif, Tk,
Mac, MFC, wxWidgets). New built-in modules are easily written in C or
C++. Python is also usable as an extension language for applications
that need a programmable interface.</p>
<p>The Python implementation is portable: it runs on many brands of UNIX,
on Windows, OS/2, Mac, Amiga, and many other platforms.</p>
<p>Some of Python's notable features: </p>
<ul>
<li>Python uses an elegant syntax for readable programs.
</li>
<li>Python is an agile language that makes it easy to get your program working. This makes Python an ideal language for prototype development and other ad-hoc programming tasks, without compromising maintainability.
</li>
<li>A variety of basic data types are available: numbers (floating point, complex, and unlimited-length long integers), strings (both ASCII and Unicode), lists, dictionaries.
</li>
<li>Python supports object-oriented programming with classes and multiple inheritance.
</li>
<li>Code can be grouped into modules and packages.
</li>
<li>The language supports raising and catching exceptions, resulting in cleaner error handling.
</li>
<li>Data types are strongly and dynamically typed. Mixing incompatible types (e.g. attempting to add a string and a number) causes an exception to be raised.
</li>
<li>Python contains advanced programming features such as generators and list comprehensions.
</li>
<li>Automatic garbage collection frees you from the hassles of memory management.
</li>
<li>The large standard library supports many common programming tasks such as connecting to web servers, regular expressions, and file handling.
</li>
<li>Python's interactive mode makes it easy to test short snippets of code. There's also a bundled development environment called IDLE.
</li>
<li>The Python interpreter is easily extended by adding new modules implemented in a compiled language such as C or C++.
</li>
<li>The interpreter can also be embedded into an application to provide a programmable interface.
</li>
<li>Python runs on many different computers and operating systems: Windows, MacOS, many brands of Unix, OS/2, ...
</li>
</ul>
<p>We will not discuss the specifics of Python here but instead refer the reader to the
<a href="http://www.python.org/">Python</a> website. Also see <a href="http://diveintopython.org/">Dive Into Python - Python from novice to pro</a>
</p>
<a name="Python_and_lpsolve"></a>
<h3>Python and lpsolve</h3>
<p>lpsolve is callable from Python via an extension or module. As such, it looks like lpsolve is fully integrated
with Python. Matrices can directly be transferred between Python and lpsolve in both directions. The complete interface
is written in C so it has maximum performance. The whole lpsolve API is implemented with some extra's specific for
Python (especially for matrix support). So you have full control to the complete lpsolve functionality via the lpsolve
Python driver.
If you find that this involves too much work to solve an lp model then you can also work via higher-level
script files that can make things a lot easier. See further in this article.
</p>
<p>Python is ideally suited to handle linear programming problems.
These are problems in which you have a quantity, depending linearly on several variables,
that you want to maximize or minimize subject to several constraints that are expressed
as linear inequalities in the same variables. If the number of variables and the number
of constraints are small, then there are numerous mathematical techniques for solving a
linear programming problem.
Indeed these techniques are often taught in high school or university level
courses in finite mathematics. But sometimes these numbers are high, or even if low,
the constants in the linear inequalities or the object expression for the quantity
to be optimised may be numerically complicated in which case a software package like
Python is required to effect a solution.</p>
<a name="Installation"></a>
<h3>Installation</h3>
<p>To make this possible, a driver program is needed: lpsolve55.pyd/lpsolve55.so.
This driver must be put in a directory known to Python and Python can call the lpsolve solver.</p>
<p>This driver calls lpsolve via the lpsolve shared library (lpsolve55.dll under Windows
and liblpsolve55.so under Unix/Linux) (archive lp_solve_5.5.2.14_dev.zip/lp_solve_5.5.2.14_dev.tar.gz). This has the advantage that the lpsolve driver doesn't have to
be recompiled when an update of lpsolve is provided. The shared library must be somewhere in the Windows path.</p>
<p>So note the difference between the Python lpsolve driver that is called lpsolve and the lpsolve library that implements the
API that is called lpsolve55.</p>
<p>There are also some Python script files (.py) as a quick start.</p>
<p>See <a href="#Install_the_lpsolve_driver">Install the lpsolve driver</a> for the installation of these files.</p>
<p>To test if everything is installed correctly, enter the following in the Python command window.</p>
<!--
<pre>>>> import lpsolve55
>>> lpsolve55.lpsolve()
</pre>
-->
<pre>>>> from lpsolve55 import *
>>> lpsolve()
</pre>
<p>If it gives the following, then everything is ok:</p>
<pre>lpsolve Python Interface version 5.5.0.6
using lpsolve version 5.5.2.14
Usage: [ret1, ret2, ...] = lpsolve('functionname', arg1, arg2, ...)
</pre>
<p>If you get the following:</p>
<pre>This application has failed to start because lpsolve55.dll was not found.
Re-installing the application may fix this problem.</pre>
<p>Or (Unix/Linux):</p>
<pre>liblpsolve55.so: cannot open shared object file: No such file or directory.</pre>
<p>Then Python can find the lpsolve driver program, but the driver program cannot find the lpsolve library
that contains the lpsolve implementation.
This library is called lpsolve55.dll under Windows and liblpsolve55.so under Unix/Linux.<br>
Under Windows, the lpsolve55.dll file must be in a directory that in the PATH environment variable.
This path can be shown via the following command in Python: !PATH<br>
It is common to place this in the WINDOWS\system32 folder.<br>
<br>
Under Unix/Linux, the liblpsolve55.so shared library must be either in the directories /lib or /usr/lib or in
a directory specified by the LD_LIBRARY_PATH environment variable.
</p>
<a name="Solve_an_lp_model_from_Python_via_lpsolve"></a>
<h3>Solve an lp model from Python via lpsolve</h3>
<p>In the following text, >>> before the Python commands is the Python prompt.
Only the text after >>> must be entered.
</p>
<p>To call an lpsolve function, the following syntax must be used:</p>
<pre>>>> [ret1, ret2, ...] = lpsolve('functionname', arg1, arg2, ...)</pre>
<p>The return values are optional and depend on the function called. functionname must always be enclosed between single
quotes to make it alphanumerical and it is case sensitive. The number and type of arguments depend on the function called.
Some functions even have a variable number of arguments and a different behaviour occurs depending on the type of the argument.
functionname can be (almost) any of the lpsolve API routines (see <a href="lp_solveAPIreference.htm">lp_solve API reference</a>)
plus some extra Python specific functions.
Most of the lpsolve API routines use or return an lprec structure. To make things more robust in Python, this structure
is replaced by a handle or the model name. The lprec structures are maintained internally by the lpsolve driver.
The handle is an incrementing number starting from 0.
Starting from driver version 5.5.0.2, it is also possible to use the model name instead of the handle.
This can of course only be done if a name is given to the model. This is done via lpsolve routine
<a href="#set_lp_name">set_lp_name</a> or by specifying the model name in routine <a href="#read_lp">read_lp</a>.
See <a href="#Using_model_name_instead_of_handle">Using model name instead of handle</a>.
</p>
<p>Almost all callable functions can be found in the <a href="lp_solveAPIreference.htm">lp_solve API reference</a>.
Some are exactly as described in the reference guide, others have a slightly different syntax to make maximum
use of the Python functionality. For example make_lp is used identical as described. But get_variables is slightly
different. In the API reference, this function has two arguments. The first the lp handle and the second the
resulting variables and this array must already be dimensioned. When lpsolve is used from Python, nothing must
be dimensioned in advance. The lpsolve driver takes care of dimensioning all return variables and they are
always returned as return value of the call to lpsolve. Never as argument to the routine. This can be a single
value as for get_objective or a matrix or vector as in get_variables.
In this case, get_variables returns a 4x1 matrix (vector) with the result of the 4 variables of the lp model.
</p>
<p>Note that you can get a usage of lpsolve, its arguments and the constants that it defines by entering the following in Python:</p>
<pre>>>> import lpsolve55
>>> help(lpsolve55)</pre>
<pre>
Help on module lpsolve55:
NAME
lpsolve55
FILE
c:\python24\lib\site-packages\lpsolve55.pyd
CLASSES
exceptions.Exception
lpsolve.error
class error(exceptions.Exception)
| Methods inherited from exceptions.Exception:
|
| __getitem__(...)
|
| __init__(...)
|
| __str__(...)
FUNCTIONS
lpsolve(...)
lpsolve('functionname', arg1, arg2, ...) -> execute lpsolve functionname with args
DATA
ANTIDEGEN_BOUNDFLIP = 512
ANTIDEGEN_COLUMNCHECK = 2
ANTIDEGEN_DURINGBB = 128
ANTIDEGEN_DYNAMIC = 64
ANTIDEGEN_FIXEDVARS = 1
ANTIDEGEN_INFEASIBLE = 32
ANTIDEGEN_LOSTFEAS = 16
ANTIDEGEN_NONE = 0
ANTIDEGEN_NUMFAILURE = 8
ANTIDEGEN_RHSPERTURB = 256
ANTIDEGEN_STALLING = 4
BRANCH_AUTOMATIC = 2
BRANCH_DEFAULT = 3
BRANCH_CEILING = 0
BRANCH_FLOOR = 1
CRASH_LEASTDEGENERATE = 3
CRASH_MOSTFEASIBLE = 2
CRASH_NONE = 0
CRITICAL = 1
DEGENERATE = 4
DETAILED = 5
EQ = 3
FEASFOUND = 12
FR = 0
FULL = 6
GE = 2
IMPORTANT = 3
IMPROVE_BBSIMPLEX = 8
IMPROVE_DUALFEAS = 2
IMPROVE_NONE = 0
IMPROVE_SOLUTION = 1
IMPROVE_THETAGAP = 4
INFEASIBLE = 2
Infinite = 1e+030
LE = 1
MSG_LPFEASIBLE = 8
MSG_LPOPTIMAL = 16
MSG_MILPBETTER = 512
MSG_MILPEQUAL = 256
MSG_MILPFEASIBLE = 128
MSG_PRESOLVE = 1
NEUTRAL = 0
NODE_AUTOORDER = 8192
NODE_BRANCHREVERSEMODE = 16
NODE_BREADTHFIRSTMODE = 4096
NODE_DEPTHFIRSTMODE = 128
NODE_DYNAMICMODE = 1024
NODE_FIRSTSELECT = 0
NODE_FRACTIONSELECT = 3
NODE_GAPSELECT = 1
NODE_GREEDYMODE = 32
NODE_GUBMODE = 512
NODE_PSEUDOCOSTMODE = 64
NODE_PSEUDOCOSTSELECT = 4
NODE_PSEUDONONINTSELECT = 5
NODE_PSEUDORATIOSELECT = 6
NODE_RANDOMIZEMODE = 256
NODE_RANGESELECT = 2
NODE_RCOSTFIXING = 16384
NODE_RESTARTMODE = 2048
NODE_STRONGINIT = 32768
NODE_USERSELECT = 7
NODE_WEIGHTREVERSEMODE = 8
NOFEASFOUND = 13
NOMEMORY = -2
NORMAL = 4
NUMFAILURE = 5
OPTIMAL = 0
PRESOLVED = 9
PRESOLVE_BOUNDS = 262144
PRESOLVE_COLDOMINATE = 16384
PRESOLVE_COLFIXDUAL = 131072
PRESOLVE_COLS = 2
PRESOLVE_DUALS = 524288
PRESOLVE_ELIMEQ2 = 256
PRESOLVE_IMPLIEDFREE = 512
PRESOLVE_IMPLIEDSLK = 65536
PRESOLVE_KNAPSACK = 128
PRESOLVE_LINDEP = 4
PRESOLVE_MERGEROWS = 32768
PRESOLVE_NONE = 0
PRESOLVE_PROBEFIX = 2048
PRESOLVE_PROBEREDUCE = 4096
PRESOLVE_REDUCEGCD = 1024
PRESOLVE_REDUCEMIP = 64
PRESOLVE_ROWDOMINATE = 8192
PRESOLVE_ROWS = 1
PRESOLVE_SENSDUALS = 1048576
PRESOLVE_SOS = 32
PRICER_DANTZIG = 1
PRICER_DEVEX = 2
PRICER_FIRSTINDEX = 0
PRICER_STEEPESTEDGE = 3
PRICE_ADAPTIVE = 32
PRICE_AUTOPARTIAL = 256
PRICE_HARRISTWOPASS = 4096
PRICE_LOOPALTERNATE = 2048
PRICE_LOOPLEFT = 1024
PRICE_MULTIPLE = 8
PRICE_PARTIAL = 16
PRICE_PRIMALFALLBACK = 4
PRICE_RANDOMIZE = 128
PRICE_TRUENORMINIT = 16384
PROCBREAK = 11
PROCFAIL = 10
SCALE_COLSONLY = 1024
SCALE_CURTISREID = 7
SCALE_DYNUPDATE = 256
SCALE_EQUILIBRATE = 64
SCALE_EXTREME = 1
SCALE_GEOMETRIC = 4
SCALE_INTEGERS = 128
SCALE_LOGARITHMIC = 16
SCALE_MEAN = 3
SCALE_NONE = 0
SCALE_POWER2 = 32
SCALE_QUADRATIC = 8
SCALE_RANGE = 2
SCALE_ROWSONLY = 512
SCALE_USERWEIGHT = 31
SEVERE = 2
SIMPLEX_DUAL_DUAL = 10
SIMPLEX_DUAL_PRIMAL = 6
SIMPLEX_PRIMAL_DUAL = 9
SIMPLEX_PRIMAL_PRIMAL = 5
SUBOPTIMAL = 1
TIMEOUT = 7
UNBOUNDED = 3
USERABORT = 6
</pre>
Also see <a href="#Using_string_constants">Using string constants</a> for an alternative.
<a name="An_example"></a>
<h3>An example</h3>
<p>(Note that you can execute this example by entering command per command as shown below or by executing script example1.
This will execute example1.py.)</p>
<pre>
>>> from lpsolve55 import *
>>> lp = lpsolve('make_lp', 0, 4)
>>> lpsolve('set_verbose', lp, IMPORTANT)
>>> ret = lpsolve('set_obj_fn', lp, [1, 3, 6.24, 0.1])
>>> ret = lpsolve('add_constraint', lp, [0, 78.26, 0, 2.9], GE, 92.3)
>>> ret = lpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], LE, 14.8)
>>> ret = lpsolve('add_constraint', lp, [12.68, 0, 0.08, 0.9], GE, 4)
>>> ret = lpsolve('set_lowbo', lp, 1, 28.6)
>>> ret = lpsolve('set_lowbo', lp, 4, 18)
>>> ret = lpsolve('set_upbo', lp, 4, 48.98)
>>> ret = lpsolve('set_col_name', lp, 1, 'COLONE')
>>> ret = lpsolve('set_col_name', lp, 2, 'COLTWO')
>>> ret = lpsolve('set_col_name', lp, 3, 'COLTHREE')
>>> ret = lpsolve('set_col_name', lp, 4, 'COLFOUR')
>>> ret = lpsolve('set_row_name', lp, 1, 'THISROW')
>>> ret = lpsolve('set_row_name', lp, 2, 'THATROW')
>>> ret = lpsolve('set_row_name', lp, 3, 'LASTROW')
>>> ret = lpsolve('write_lp', lp, 'a.lp')
>>> print(lpsolve('get_mat', lp, 1, 2))
78.26
>>> lpsolve('solve', lp)
0L
>>> print(lpsolve('get_objective', lp))
31.7827586207
>>> print(lpsolve('get_variables', lp)[0])
[28.600000000000001, 0.0, 0.0, 31.827586206896552]
>>> print(lpsolve('get_constraints', lp)[0])
[92.299999999999997, 6.863999999999999, 391.2928275862069]
</pre>
<p>Note that there are commands that return an answer. If they do and their result is not stored in a
variable, then it is echoed on screen. If assigned to a variable then the value is not echoed. For example:
</p>
<pre>>>> obj = lpsolve('get_objective', lp)
</pre>
<p>The result in then not shown on screen. But the contents of the variable can be printed:</p>
<pre>>>> print(obj)
31.7827586207</pre>
<p>Or even:</p>
<pre>>>> obj
31.782758620689656</pre>
<p>Note that get_variables and get_constraints return two results: The result vector and a status. If only the
vector is needed, then [0] can be used as in the example. Or the result can be stored in an extra variables:</p>
<pre>
>>> [x, ret] = lpsolve('get_variables', lp)
</pre>
<p>Variable x will contain the result vector and ret the return status of the call.</p>
<p>Note that if this is stored only in one variable that you get the following:</p>
<pre>
>>> x = lpsolve('get_variables', lp)
>>> print(x)
[[28.600000000000001, 0.0, 0.0, 31.827586206896552], 1L]
</pre>
<p>Don't forget to free the handle and its associated memory when you are done:</p>
<pre>>>> lpsolve('delete_lp', lp)</pre>
<p>Note that there is another way to access the lpsolve library. It is more object oriented, but requires more typing:</p>
<pre>>>> import lpsolve55
>>> lp = lpsolve55.lpsolve('make_lp', 0, 4)
>>> lpsolve55.lpsolve('set_verbose', lp, lpsolve55.IMPORTANT)
.
.
.
>>> lpsolve55.lpsolve('delete_lp', lp)</pre>
<p>This technique will not be used in this description because the lpsolve library is not really object oriented structured.
But if you prefer it, there is nothing that should stop you.
The only difference is that you have to put lpsolve55. before every lpsolve function and constant.</p>
<a name="Using_model_name_instead_of_handle"></a>
<h3>Using model name instead of handle</h3>
From driver version 5.5.0.2, it is possible to use the model name instead of the handle. From the moment the model
has a name, you can use this name instead of the handle. This is best shown by an example. Above example would look
like this:
<pre>
>>> from lpsolve55 import *
>>> lp = lpsolve('make_lp', 0, 4)
>>> ret = lpsolve('set_lp_name', lp, 'mymodel')
>>> lpsolve('set_verbose', 'mymodel', IMPORTANT)
>>> ret = lpsolve('set_obj_fn', 'mymodel', [1, 3, 6.24, 0.1])
>>> ret = lpsolve('add_constraint', 'mymodel', [0, 78.26, 0, 2.9], GE, 92.3)
>>> ret = lpsolve('add_constraint', 'mymodel', [0.24, 0, 11.31, 0], LE, 14.8)
>>> ret = lpsolve('add_constraint', 'mymodel', [12.68, 0, 0.08, 0.9], GE, 4)
>>> ret = lpsolve('set_lowbo', 'mymodel', 1, 28.6)
>>> ret = lpsolve('set_lowbo', 'mymodel', 4, 18)
>>> ret = lpsolve('set_upbo', 'mymodel', 4, 48.98)
>>> ret = lpsolve('set_col_name', 'mymodel', 1, 'COLONE')
>>> ret = lpsolve('set_col_name', 'mymodel', 2, 'COLTWO')
>>> ret = lpsolve('set_col_name', 'mymodel', 3, 'COLTHREE')
>>> ret = lpsolve('set_col_name', 'mymodel', 4, 'COLFOUR')
>>> ret = lpsolve('set_row_name', 'mymodel', 1, 'THISROW')
>>> ret = lpsolve('set_row_name', 'mymodel', 2, 'THATROW')
>>> ret = lpsolve('set_row_name', 'mymodel', 3, 'LASTROW')
>>> ret = lpsolve('write_lp', 'mymodel', 'a.lp')
>>> print(lpsolve('get_mat', 'mymodel', 1, 2))
78.26
>>> lpsolve('solve', 'mymodel')
0L
>>> print(lpsolve('get_objective', 'mymodel'))
31.7827586207
>>> print(lpsolve('get_variables', 'mymodel')[0])
[28.600000000000001, 0.0, 0.0, 31.827586206896552]
>>> print(lpsolve('get_constraints', 'mymodel')[0])
[92.299999999999997, 6.863999999999999, 391.2928275862069]
</pre>
<p>So everywhere a handle is needed, you can also use the model name. You can even mix the two methods.
There is also a specific Python routine to get the handle from the model name: <a href="#get_handle">get_handle</a>.<br>
For example:</p>
<pre>
>>> lp = lpsolve('get_handle', 'mymodel')
>>> print(lp)
0
</pre>
<p>Don't forget to free the handle and its associated memory when you are done:</p>
<pre>>>> lpsolve('delete_lp', 'mymodel')</pre>
<p>In the next part of this documentation, the handle is used. But if you name the model, the name could thus also be used.</p>
<a name="Matrices"></a>
<h3>Matrices</h3>
lpsolve uses Python lists to represent matrices (and vectors). Note that lpsolve can only work with real numbers, not complex numbers.
For example:
<pre>>>> lpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], 1, 14.8)</pre>
<p>[0.24, 0, 11.31, 0] is a list type variable.</p>
<p>Most of the time, variables are used to provide the data:</p>
<pre>>>> lpsolve('add_constraint', lp, a1, 1, 14.8)</pre>
<p>Where a1 is a variable of type list. Sometimes a two-dimensional matrix is used:</p>
<pre>>>> lpsolve('set_mat', lp, [[1, 2, 3], [4, 5, 6]])</pre>
<p>[1, 2, 3] is the first row and [4, 5, 6] is the second row.</p>
<p>The lpsolve driver sees all provided matrices as sparse matrices. lpsolve uses sparse matrices
internally and data can be provided sparse via the ex routines. For example add_constraintex. The lpsolve
driver always uses the ex routines to provide the data to lpsolve. Even if you call from Python the routine
names that would require a dense matrix (for example add_constraint), the lpsolve driver will always call the
sparse version of the routine (for example add_constraintex). This results in the most performing behaviour.
Matrices with too few or too much elements gives an 'invalid vector.' error.</p>
<p>An important final note. Several lp_solve API routines accept a vector where the first element (element 0) is not used.
Other lp_solve API calls do use the first element. In the Python interface, there is never an unused element in the matrices.
So if the lp_solve API specifies that the first element is not used, then this element is not in the Python matrix.</p>
<a name="Maximum_usage_of_matrices_with_lpsolve"></a>
<h3>Maximum usage of matrices with lpsolve</h3>
<p>Because Python has the list possibility to represent vectors, all lpsolve API routines that need a column or row number to get/set information for that
column/row are extended in the lpsolve Python driver to also work with vectors. For example set_int in the API can
only set the integer status for one column. If the status for several integer variables must be set, then set_int
must be called multiple times. The lpsolve Python driver however also allows specifying a vector to set the integer
status of all variables at once. The API call is: return = lpsolve('set_int', lp, column, must_be_int). The
matrix version of this call is: return = lpsolve('set_int', lp, [must_be_int]).
The API call to return the integer status of a variable is: return = lpsolve('is_int', lp, column). The
matrix version of this call is: [is_int] = lpsolve('is_int', lp)<br>
Also note the get_mat and set_mat routines. In Python these are extended to return/set the complete constraint matrix.
See following example.
</p>
<p>Above example can thus also be done as follows:<br>
(Note that you can execute this example by entering command per command as shown below or by executing script example2.
This will execute example2.py.)
</p>
<pre>>>> lp = lpsolve('make_lp', 0, 4)
>>> lpsolve('set_verbose', lp, IMPORTANT)
>>> ret = lpsolve('set_obj_fn', lp, [1, 3, 6.24, 0.1])
>>> ret = lpsolve('add_constraint', lp, [0, 78.26, 0, 2.9], GE, 92.3)
>>> ret = lpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], LE, 14.8)
>>> ret = lpsolve('add_constraint', lp, [12.68, 0, 0.08, 0.9], GE, 4)
>>> ret = lpsolve('set_lowbo', lp, [28.6, 0, 0, 18])
>>> ret = lpsolve('set_upbo', lp, [Infinite, Infinite, Infinite, 48.98])
>>> ret = lpsolve('set_col_name', lp, ['COLONE', 'COLTWO', 'COLTHREE', 'COLFOUR'])
>>> ret = lpsolve('set_row_name', lp, ['THISROW', 'THATROW', 'LASTROW'])
>>> ret = lpsolve('write_lp', lp, 'a.lp')
>>> print(lpsolve('get_mat', lp)[0])
[[0.0, 78.26, 0.0, 2.9], [0.24, 0.0, 11.31, 0.0], [12.68, 0.0, 0.08, 0.9]]
>>> lpsolve('solve', lp)
0L
>>> print(lpsolve('get_objective', lp))
31.7827586207
>>> print(lpsolve('get_variables', lp)[0])
[28.600000000000001, 0.0, 0.0, 31.827586206896552]
>>> print(lpsolve('get_constraints', lp)[0])
[92.299999999999997, 6.8639999999999999, 391.29282758620695]
</pre>
<p>Note the usage of Infinite in set_upbo. This stands for 'infinity'. Meaning an infinite upper bound.
It is also possible to use -Infinite to express minus infinity. This can for example be used to create a free variable.
Infinite is a constant defined by the lpsolve library.</p>
<p>To show the full power of the matrices, let's now do some matrix calculations to check the solution.
It works further on above example. Note that Python doesn't support matrix calculations on lists.
However, there are several numerical packages that can do this. The list type variables must be converted to
the matrix types of these packages. Two common known packages for this are Numeric and numpy.
These are not installed by default but can be easily installed.
See <a href="http://sourceforge.net/project/showfiles.php?group_id=1369&package_id=1351">http://sourceforge.net/project/showfiles.php?group_id=1369&package_id=1351</a> and
<a href="http://sourceforge.net/projects/numpy/files/">http://sourceforge.net/projects/numpy/files/</a>.
See <a href="http://numpy.scipy.org/">http://numpy.scipy.org/</a> for a brief overview.</p>
<pre>>>> from numpy import *</pre>
or
<pre>>>> from Numeric import *</pre>
<p>This documentation works with numpy, but Numeric can be used also.</p>
<pre>>>> from numpy import *
>>> A = array(lpsolve('get_mat', lp)[0])
>>> A
array([[ 0. , 78.26, 0. , 2.9 ],
[ 0.24, 0. , 11.31, 0. ],
[ 12.68, 0. , 0.08, 0.9 ]])
>>> X = array(lpsolve('get_variables', lp)[0])
>>> X
array([ 28.6 , 0. , 0. , 31.82758621])
>>> B = dot(A, X)
>>> B
array([ 92.3 , 6.864 , 391.29282759])
</pre>
<p>We even don't have to explicitly convert the lists to matrices:</p>
<pre>>>> from numpy import *
>>> a = lpsolve('get_mat', lp)[0]
>>> a
[[0.0, 78.26, 0.0, 2.9], [0.24, 0.0, 11.31, 0.0], [12.681, 0.0, 0.018, 0.9]]
>>> x = lpsolve('get_variables', lp)[0]
>>> x
[28.600000000000001, 0.0, 0.0, 31.827586206896552]
>>> B = dot(a, x)
>>> B
array([ 92.3 , 6.864 , 391.29282759])
</pre>
<p>dot returns not a list, but an array object.
If the result is needed again in a list, then this can be easily done:</p>
<pre>>>> b = list(B)
>>> b
[92.299999999999997, 6.8639999999999999, 391.29282758620695]
</pre>
<p>So what we have done here is calculate the values of the constraints (RHS) by multiplying the constraint matrix
with the solution vector. Now take a look at the values of the constraints that lpsolve has found:</p>
<pre>>>> lpsolve('get_constraints', lp)[0]
[92.299999999999997, 6.8639999999999999, 391.29282758620695]
</pre>
<p>Exactly the same as the calculated B vector, as expected.</p>
<p>Also the value of the objective can be calculated in a same way:</p>
<pre>>>> c = lpsolve('get_obj_fn', lp)[0]
>>> x = lpsolve('get_variables', lp)[0]
>>> obj = dot(c, x)
>>> obj
31.782758620689656
</pre>
<p>So what we have done here is calculate the value of the objective by multiplying the objective vector
with the solution vector. Now take a look at the value of the objective that lpsolve has found:</p>
<pre>>>> lpsolve('get_objective', lp)
31.782758620689656
</pre>
<p>Again exactly the same as the calculated obj value, as expected.</p>
<a name="numpy_package"></a>
<h3>numpy package</h3>
In the above section <a href="#Maximum_usage_of_matrices_with_lpsolve">Maximum usage of matrices with lpsolve</a> the
package numpy was already mentioned. See <a href="http://numpy.scipy.org/">http://numpy.scipy.org/</a> for a brief overview.
This package is the successor of the older and obsolete package Numeric.
Since lp_solve is all about arrays and matrices, it is logical that the lpsolve Python driver accepts numpy arrays.
This is possible from driver version 5.5.0.9. Before it was needed that numpy arrays were converted to lists.<br>
For example:
<pre>>>> from numpy import *
>>> from lpsolve55 import *
>>> lp=lpsolve('make_lp', 0, 4);
>>> c = array([1, 3, 6.24, 0.1])
>>> ret = lpsolve('set_obj_fn', lp, c)
</pre>
Note that the numpy array variable c is passed directly to lpsolve.
Before driver version 5.5.0.9 this gave an error since lpsolve did not know numpy arrays.
They had to be converted to lists:
<pre>>>> ret = lpsolve('set_obj_fn', lp, list(c))</pre>
<p>That is ok for small models, but for larger arrays this gives an extra memory overhead since c is now two times in
memory. Once as the numpy array and once as list.</p>
<p>Note that all returned arrays from lpsolve are always lists.</p>
<p>Also note that the older package Numeric is not supported by lpsolve.
So it is not possible to provide a Numeric array to lpsolve. That will give an error.</p>
<a name="Using_string_constants"></a>
<h3>Using string constants</h3>
From driver version 5.5.2.14 on, it is possible to use string constants
everywhere an lp_solve constant is needed or returned. This is best shown by an example.
In the above code we had:
<pre>>>> lp=lpsolve('make_lp', 0, 4);
>>> lpsolve('set_verbose', lp, IMPORTANT);
>>> ret = lpsolve('add_constraint', lp, [0, 78.26, 0, 2.9], GE, 92.3);
>>> ret = lpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], LE, 14.8);
>>> lpsolve('add_constraint', lp, [12.68, 0, 0.08, 0.9], GE, 4);</pre>
<p>Note the 3rd parameter on set_verbose and the 4th on add_constraint. These are
lp_solve constants. One can define all the possible constants in Python as is
done in the Python driver and
then use them in the calls, but that has several disadvantages. First there
stays the possibility to provide a constant that is not intended for that
particular call. Another issue is that calls that return a constant are still
returning it numerical.</p>
<p>Both issues can now be handled by string constants. The above code can be done as
following with string constants:</p>
<pre>>>> lp=lpsolve('make_lp', 0, 4);
>>> lpsolve('set_verbose', lp, 'IMPORTANT');
>>> ret = lpsolve('add_constraint', lp, [0, 78.26, 0, 2.9], 'GE', 92.3);
>>> ret = lpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], 'LE', 14.8);
>>> ret = lpsolve('add_constraint', lp, [12.68, 0, 0.08, 0.9], 'GE', 4);</pre>
<p>This is not only more readable, there is much lesser chance that mistakes are
being made. The calling routine knows which constants are possible and only
allows these. So unknown constants or constants that are intended for other
calls are not accepted. For example:</p>
<pre>>>> lpsolve('set_verbose', lp, 'blabla');
Traceback (most recent call last):
File "<pyshell#25>", line 1, in <module>
lpsolve('set_verbose', lp, 'blabla');
error: BLABLA: Unknown.
>>> lpsolve('set_verbose', lp, 'GE');
Traceback (most recent call last):
File "<pyshell#26>", line 1, in <module>
lpsolve('set_verbose', lp, 'GE');
error: GE: Not allowed here.</pre>
<p>Note the difference between the two error messages. The first says that the
constant is not known, the second that the constant cannot be used at that
place.</p>
<p>Constants are case insensitive. Internally they are always translated to upper
case. Also when returned they will always be in upper case.</p>
<p>The constant names are the ones as specified in the documentation of each API
routine. There are only 3 exceptions, extensions actually. 'LE', 'GE' and 'EQ' in
<a href="add_constraint.htm">add_constraint</a> and <a href="is_constr_type.htm">is_constr_type</a>
can also be '<', '<=', '>', '>=', '='. When returned however, 'GE', 'LE', 'EQ'
will be used.</p>
<p>Also in the matrix version of calls, string constants are possible. For example:</p>
<pre>>>> ret = lpsolve('set_constr_type', lp, ['LE', 'EQ', 'GE']);</pre>
<p>Some constants can be a combination of multiple constants. For example
<a href="set_scaling.htm">set_scaling</a>:</p>
<pre>>>> lpsolve('set_scaling', lp, 3+128);</pre>
<p>With the string version of constants this can be done as following:</p>
<pre>>>> lpsolve('set_scaling', lp, 'SCALE_MEAN|SCALE_INTEGERS');</pre>
<p>| is the OR operator used to combine multiple constants. There may optinally be
spaces before and after the |.</p>
<p>Not all OR combinations are legal. For example in set_scaling, a choice must be
made between SCALE_EXTREME, SCALE_RANGE, SCALE_MEAN, SCALE_GEOMETRIC or
SCALE_CURTISREID. They may not be combined with each other. This is also tested:</p>
<pre>>>> lpsolve('set_scaling', lp, 'SCALE_MEAN|SCALE_RANGE');
Traceback (most recent call last):
File "<pyshell#32>", line 1, in <module>
lpsolve('set_scaling', lp, 'SCALE_MEAN|SCALE_RANGE');
error: SCALE_RANGE cannot be combined with SCALE_MEAN</pre>
<p>Everywhere constants must be provided, numeric or string values may be provided.
The routine automatically interpretes them. </p>
<p>Returning constants is a different
story. The user must let lp_solve know how to return it. Numerical or as string.
The default is numerical:</p>
<pre>>>> lpsolve('get_scaling', lp)
131L</pre>
<p>To let lp_solve return a constant as string, a call to a new function must be
made: return_constants</p>
<pre>>>> ret = lpsolve('return_constants', 1);</pre>
<p>From now on, all returned constants are returned as string:</p>
<pre>>>> lpsolve('get_scaling', lp)
'SCALE_MEAN|SCALE_INTEGERS'</pre>
<p>Also when an array of constants is returned, they are returned as string when
return_constants is set:</p>
<pre>>>> lpsolve('get_constr_type', lp)
['LE', 'EQ', 'GE']</pre>
<p>This for all routines until return_constants is again called with 0:</p>
<pre>>>> ret = lpsolve('return_constants', 0);</pre>
<p>The (new) current setting of return_constants is always returned by the call.
Even when set:</p>
<pre>>>> lpsolve('return_constants', 1)
1L</pre>
<p>To get the value without setting it, don't provide the second argument:</p>
<pre>>>> lpsolve('return_constants')
1L</pre>
<p>In the next part of this documentation, return_constants is the default, 0, so all
constants are returned numerical and provided constants are also numerical. This
to keep the documentation as compatible as possible with older versions. But
don't let you hold that back to use string constants in your code.</p>
<a name="Callbacks"></a>
<h3>Callbacks</h3>
<p>lp_solve has a callback mechanisms to Python while it is in the solve process.
To enable this, a python routine must be registered to lp_solve and it will then be called when needed.
Following callbacks are possible:</p>
<TABLE id="Table2" cellSpacing="1" cellPadding="1" width="100%" border="1">
<TR>
<TH>Callback functionality</TH>
<TH width=450>Python example</TH>
<TH>See</TH>
</TR>
<TR>
<TD>Sets an abort routine.</TD>
<TD>lpsolve('put_abortfunc', lp, abortfunc, "extra")</TD>
<TD><a href="put_abortfunc.htm">put_abortfunc</a></TD>
</TR>
<TR>
<TD>Sets a log routine.</TD>
<TD>lpsolve('put_logfunc', lp, logfunc, "extra")</TD>
<TD><a href="put_logfunc.htm">put_logfunc</a></TD>
</TR>
<TR>
<TD>Sets a message routine.</TD>
<TD>lpsolve('put_msgfunc', lp, msgfunc, "extra", 1023)</TD>
<TD><a href="put_msgfunc.htm">put_msgfunc</a></TD>
</TR>
<TR>
<TD>Specifies a user function to select a B&B branching, given the column to branch on.</TD>
<TD>lpsolve('put_bb_branchfunc', lp, branchfunc, "extra")</TD>
<TD><a href="put_bb_branchfunc.htm">put_bb_branchfunc</a></TD>
</TR>
<TR>
<TD>Allows to set a user function that specifies which non-integer variable to select next to make integer in the B&B solve.</TD>
<TD>lpsolve('put_bb_nodefunc', lp, nodefunc, "extra")</TD>
<TD><a href="put_bb_nodefunc.htm">put_bb_nodefunc</a></TD>
</TR>
</TABLE>
<p>Note that the callback routine *must* have the same parameter list as required by the callback routine for the put_* routine.
If that is not the case it is likely that the program will crash. There is no check done by lp_solve that this is the case.
</p>
<p>Example:</p>
<pre>
>>> from lpsolve55 import *
>>> lp = lpsolve('make_lp', 0, 4)
>>> lpsolve('set_obj_fn', lp, [1, 3, 6.24, 0.1])
>>> lpsolve('add_constraint', lp, [0, 78.26, 0, 2.9], GE, 92.3)
>>> lpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], LE, 14.8)
>>> lpsolve('add_constraint', lp, [12.68, 0, 0.08, 0.9], GE, 4)
>>> lpsolve('set_lowbo', lp, 1, 28.6)
>>> lpsolve('set_lowbo', lp, 4, 18)
>>> lpsolve('set_upbo', lp, 4, 48.98)
>>> lpsolve('set_int', lp, [1, 1, 1, 1])
>>> def abortfunc(lp, userhandle): print("abortfunc(%d, %s)" % (lp, userhandle)); return 0
>>> lpsolve('put_abortfunc', lp, abortfunc, "abortfunc")
>>> def logfunc(lp, userhandle, buf): print("logfunc(%d, %s, %s)" % (lp, userhandle, buf)); return 0
>>> lpsolve('put_logfunc', lp, logfunc, "logfunc")
>>> def msgfunc(lp, userhandle, message): print("msgfunc(%d, %s %d)" % (lp, userhandle, message)); return 0
>>> lpsolve('put_msgfunc', lp, msgfunc, "msgfunc", 1023)
>>> def branchfunc(lp, branchhandle, column): print("branchfunc(%d, %s, %d)" % (lp, branchhandle, column)); return 0
>>> lpsolve('put_bb_branchfunc', lp, branchfunc, "branchfunc")
>>> def nodefunc(lp, nodehandle, vartype): print("nodefunc(%d, %s, %d)" % (lp, nodehandle, vartype)); return -1
>>> lpsolve('put_bb_nodefunc', lp, nodefunc, "nodefunc")
>>> lpsolve('solve', lp)
>>> lpsolve('delete_lp', lp)
</pre>
<a name="py-files"></a>
<h3>py-files</h3>
<p>Python can execute a sequence of statements stored in diskfiles. Such files are called
Python scripts and should have the file type of ".py" as the last part of their filename (extension).</p>
<p>You can put Python commands in them and execute them at
any time. The Python script is executed either via the command python script.py.
The script files contain plain ascii data.</p>
<p>The lpsolve Python distribution contains some example script to demonstrate this.</p>
<h4>example1.py</h4>
<p>Contains the commands as shown in the first example of this article.</p>
<h4>example2.py</h4>
<p>Contains the commands as shown in the second example of this article.</p>
<h4>example3.py</h4>
<p>Contains the commands of a practical example. See further in this article.</p>
<h4>example4.py</h4>
<p>Contains the commands of a practical example. See further in this article.</p>
<h4>example5.py</h4>
<p>Contains the commands of a practical example. See further in this article.</p>
<h4>example6.py</h4>
<p>Contains the commands of a practical example. See further in this article.</p>
<h4>lp_solve.py</h4>
<p>This script uses the API to create a higher-level function called lp_solve.
This function accepts as arguments some matrices and options to create and solve an lp model.
Type help(lp_solve) or just lp_solve() to see its usage:</p>
<pre> LP_SOLVE Solves mixed integer linear programming problems.
SYNOPSIS: [obj,x,duals] = lp_solve(f,a,b,e,vlb,vub,xint,scalemode,keep)
solves the MILP problem
max v = f'*x
a*x <> b
vlb <= x <= vub
x(int) are integer
ARGUMENTS: The first four arguments are required:
f: n vector of coefficients for a linear objective function.
a: m by n matrix representing linear constraints.
b: m vector of right sides for the inequality constraints.
e: m vector that determines the sense of the inequalities:
e(i) = -1 ==> Less Than
e(i) = 0 ==> Equals
e(i) = 1 ==> Greater Than
vlb: n vector of lower bounds. If empty or omitted,
then the lower bounds are set to zero.
vub: n vector of upper bounds. May be omitted or empty.
xint: vector of integer variables. May be omitted or empty.
scalemode: scale flag. Off when 0 or omitted.
keep: Flag for keeping the lp problem after it's been solved.
If omitted, the lp will be deleted when solved.
OUTPUT: A nonempty output is returned if a solution is found:
obj: Optimal value of the objective function.
x: Optimal value of the decision variables.
duals: solution of the dual problem.
</pre>
<p>Example of usage. To create and solve following lp-model:</p>
<pre>max: -x1 + 2 x2;
C1: 2x1 + x2 < 5;
-4 x1 + 4 x2 <5;
int x2,x1;
</pre>
<p>The following command can be used:</p>
<pre>>>> from lp_solve import *
>>> [obj, x, duals] = lp_solve([-1, 2], [[2, 1], [-4, 4]], [5, 5], [-1, -1], None, None, [1, 2])
>>> print(obj)
3.0
>>> print(x)
[1.0, 2.0]
</pre>
<h4>lp_maker.py</h4>
<p>This script is analog to the lp_solve script and also uses the API to create a higher-level function called lp_maker.
This function accepts as arguments some matrices and options to create an lp model. Note that this scripts only
creates a model and returns a handle.
Type help(lp_maker) or just lp_maker() to see its usage:</p>
<pre>
LP_MAKER Makes mixed integer linear programming problems.
SYNOPSIS: lp_handle = lp_maker(f,a,b,e,vlb,vub,xint,scalemode,setminim)
make the MILP problem
max v = f'*x
a*x <> b
vlb <= x <= vub
x(int) are integer
ARGUMENTS: The first four arguments are required:
f: n vector of coefficients for a linear objective function.
a: m by n matrix representing linear constraints.
b: m vector of right sides for the inequality constraints.
e: m vector that determines the sense of the inequalities:
e(i) < 0 ==> Less Than
e(i) = 0 ==> Equals
e(i) > 0 ==> Greater Than