# Using lpsolve from O-Matrix

### O-Matrix?

O-Matrix is an integrated environment for analysing and visualizing data, and building turnkey scientific and engineering computing solutions. The program includes hundreds of engineering and statistical functions for solving a broad range of technical computing problems. Easy-to-use and flexible plotting commands enable you to rapidly build design prototypes, and implement sophisticated systems.

The foundation of O-Matrix is a high-performance matrix language that is specifically designed for high-performance technical computing. The notation of this language will dramatically reduce your design and implementation efforts, and enable the construction of systems that execute far quicker than other interpreted environments. O-Matrix also provides a compatibility mode that enables you to run MATLABŠ m-files. This enables you to leverage existing m-files, and simplifies the transition to O-Matrix for users experienced with MATLAB.

The O-Matrix environment is interpreted which means your commands are immediately executed as you enter them. Textual output is displayed in the Command window, and plotting commands are displayed in one or more Graphic windows. The environment provides a debugger for debugging, analysing, and profiling complex algorithms.

We will not discuss the specifics of O-Matrix here but instead refer the reader to the O-Matrix website.

### O-Matrix and lpsolve

lpsolve is callable from O-Matrix via a dynamic linked DLL function. As such, it looks like lpsolve is fully integrated with O-Matrix. Matrices can directly be transferred between O-Matrix 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 O-Matrix (especially for matrix support). So you have full control to the complete lpsolve functionality via the omlpsolve O-Matrix 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.

### Quickstart

    Compile and build omlpsolve:
    ----------------------------

    1. Under Windows, the Microsoft Visual C/C++ compiler must be installed
       and the environment variables must be active do that when a command prompt
       is opened, the cl and nmake commands can be executed.

    2. Go to directory lp_solve_5.5\extra\O-Matrix\lpsolve

    3. To compile and build omlpsolve, enter the following command:
          cvc

    Load the omlpsolve driver in the O-Matrix memory space:
    -------------------------------------------------------

    1. Under Windows, make sure that the lpsolve55.dll file is somewhere in the path
       (archive lp_solve_5.5.0.14_dev.zip)

    2. A precompiled library is provided for Windows (omlpsolve.dll).

    3. Start O-Matrix

    4. Enter the following command in O-Matrix:
          O> dll <path>\omlpsolve.dll, omlpsolve
       This can also be added in autoexec.oms to automatically load the omlpsolve driver.

Note that O-Matrix version 5.8 or above is strongly recommended. Lower versions (at least 5.7) should work with this driver, but these versions don't have the ability to print information on the command prompt. For example default while a solve is done, information is printed to the command window. This will only be visible from version 5.8 or above.

O-Matrix 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 optimized may be numerically complicated in which case a software package like O-Matrix is required to effect a solution.

### Installation

To make this possible, a driver program is needed: omlpsolve (omlpsolve.dll under Windows). This driver must be loaded in O-Matrix and O-Matrix can call the omlpsolve solver.

This driver calls lpsolve via the lpsolve shared library (lpsolve55.dll under Windows). This has the advantage that the omlpsolve driver doesn't have to be recompiled when an update of lpsolve is provided. The shared library must be somewhere in the Windows path.

So note the difference between the O-Matrix lpsolve driver that is called omlpsolve and the lpsolve library that implements the API that is called lpsolve55.

There are also some O-Matrix script files (.oms) as a quick start.

The first thing that must be done, each time O-Matrix is restarted and you want to use lpsolve is load the omlpsolve driver into the O-Matrix workspace. This is done via the dll command. Suppose that omlpsolve.dll is installed in c:\omwin\dll, then the following command must be used to load the driver:

    dll c:\omwin\dll\omlpsolve.dll, omlpsolve

That is basically all you need to do. From now on, you can use the library. This until a clear command is given or O-Matrix is restarted. Then this command must be given again to reload the library.

To make things easier, you can edit the file autoexec.oms with your favourite editor (or notepad) in the omwin folder and add above line at the end of this file (before the last end). That will automatically load the lpsolve driver in memory when O-Matrix is started and also when a clear command is executed. So it will appear as if the omlpsolve command is then always available.

To test if everything is installed correctly, enter omlpsolve in the O-Matrix command prompt. If it gives the following, then everything is ok:

    omlpsolve O-Matrix Interface version 5.5.0.6
    using lpsolve version 5.5.0.14

    Usage: [ret1, ret2, ...] = omlpsolve("functionname", arg1, arg2, ...)

Possibly, this is followed with:

    No printing capability to command window available.
    You need to upgrade to version 5.8 for this feature.

Then you are working with an O-Matrix version lower than 5.8. The driver should work, but nothing is printed on the command window when lpsolve has something to report (for example while solving).

However, if you get a message box with the following:

    The identifier omlpsolve is not defined.

Then either the dll command that was previous given was unsuccessful (or not given at all) or something was misspelled after the ,

If you get the following:

    This application has failed to start because lpsolve55.dll was not found.
    Re-installing the application may fix this problem.

Then O-Matrix can find the omlpsolve driver program, but the driver program cannot find the lpsolve library that contains the lpsolve implementation. This library is called lpsolve55.dll and should be on your system in a directory that in the PATH environment variable. This path can be shown via the command getenv("PATH")

The lpsolve55.dll files must be in one of these specified directories. It is common to place this in the WINDOWS\system32 folder.

All this is developed and tested with O-Matrix version 5.7. This is the minimum supported release. Older releases are unsupported.

### Solve an lp model from O-Matrix via omlpsolve

In the following text, O> before the O-Matrix commands is the O-Matrix command line. Only the text after O> must be entered.

To call an lpsolve function, the following syntax must be used:

    O> [ret1, ret2, ...] = omlpsolve("functionname", arg1, arg2, ...)

The return values are optional and depend on the function called. functionname must always be enclosed between double 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 lp_solve API reference) plus some extra O-Matrix specific functions. Most of the lpsolve API routines use or return an lprec structure. To make things more robust in O-Matrix, 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 set_lp_name or by specifying the model name in routine read_lp. See Using model name instead of handle.

Almost all callable functions can be found in the lp_solve API reference. Some are exactly as described in the reference guide, others have a slightly different syntax to make maximum use of the O-Matrix 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 O-Matrix, nothing must be dimensioned in advance. The omlpsolve driver takes care of dimensioning all return variables and they are always returned as return value of the call to omlpsolve. Never as argument to the routine. This can be a single value as for get_objective (although O-Matrix stores this in a 1x1 matrix) 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.

### An example

(Note that you can execute this example by entering command per command as shown below or by just entering example1. This will execute example1.oms.)

    O> lp=omlpsolve("make_lp", 0, 4);
    O> omlpsolve("set_verbose", lp, 3);
    O> omlpsolve("set_obj_fn", lp, [1, 3, 6.24, 0.1]);
    O> omlpsolve("add_constraint", lp, [0, 78.26, 0, 2.9], 2, 92.3);
    O> omlpsolve("add_constraint", lp, [0.24, 0, 11.31, 0], 1, 14.8);
    O> omlpsolve("add_constraint", lp, [12.68, 0, 0.08, 0.9], 2, 4);
    O> omlpsolve("set_lowbo", lp, 1, 28.6);
    O> omlpsolve("set_lowbo", lp, 4, 18);
    O> omlpsolve("set_upbo", lp, 4, 48.98);
    O> omlpsolve("set_col_name", lp, 1, "COLONE");
    O> omlpsolve("set_col_name", lp, 2, "COLTWO");
    O> omlpsolve("set_col_name", lp, 3, "COLTHREE");
    O> omlpsolve("set_col_name", lp, 4, "COLFOUR");
    O> omlpsolve("set_row_name", lp, 1, "THISROW");
    O> omlpsolve("set_row_name", lp, 2, "THATROW");
    O> omlpsolve("set_row_name", lp, 3, "LASTROW");
    O> omlpsolve("write_lp", lp, "a.lp");
    O> omlpsolve("get_mat", lp, 1, 2)
       78.2600
    O> omlpsolve("solve", lp)
         0
    O> omlpsolve("get_objective", lp)
       31.7828
    O> omlpsolve("get_variables", lp)
    {
    28.6
    0
    0
    31.8276
    }

    O> omlpsolve("get_constraints", lp)
    {
    92.3
    6.8640
    391.293
    }

Note that there are some commands that return an answer. To see the answer, the command was not terminated with a semicolon (;). If the semicolon is put at the end of a command, the answer is not shown. However it is also possible to write the answer in a variable. In that case the result is never shown. With or without a terminating semicolon. For example:

    O> obj=omlpsolve("get_objective", lp)

Or:

    O> obj=omlpsolve("get_objective", lp);

Both will only write the result in variable obj without showing anything on screen. get_variables and get_constraints return a vector with the result. This can also be put in a variable:

    O> x=omlpsolve("get_variables", lp);
    O> b=omlpsolve("get_constraints", lp);

It is always possible to show the contents of a variable by just giving it as command:

    O> x
    {
    28.6
    0
    0
    31.8276
    }

Don't forget to free the handle and its associated memory when you are done:

    O> omlpsolve("delete_lp", lp);

### Using model name instead of handle

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:

    O> lp=omlpsolve("make_lp", 0, 4);
    O> omlpsolve("set_lp_name", lp, "mymodel");
    O> omlpsolve("set_verbose", "mymodel", 3);
    O> omlpsolve("set_obj_fn", "mymodel", [1, 3, 6.24, 0.1]);
    O> omlpsolve("add_constraint", "mymodel", [0, 78.26, 0, 2.9], 2, 92.3);
    O> omlpsolve("add_constraint", "mymodel", [0.24, 0, 11.31, 0], 1, 14.8);
    O> omlpsolve("add_constraint", "mymodel", [12.68, 0, 0.08, 0.9], 2, 4);
    O> omlpsolve("set_lowbo", "mymodel", 1, 28.6);
    O> omlpsolve("set_lowbo", "mymodel", 4, 18);
    O> omlpsolve("set_upbo", "mymodel", 4, 48.98);
    O> omlpsolve("set_col_name", "mymodel", 1, "COLONE");
    O> omlpsolve("set_col_name", "mymodel", 2, "COLTWO");
    O> omlpsolve("set_col_name", "mymodel", 3, "COLTHREE");
    O> omlpsolve("set_col_name", "mymodel", 4, "COLFOUR");
    O> omlpsolve("set_row_name", "mymodel", 1, "THISROW");
    O> omlpsolve("set_row_name", "mymodel", 2, "THATROW");
    O> omlpsolve("set_row_name", "mymodel", 3, "LASTROW");
    O> omlpsolve("write_lp", "mymodel", "a.lp");
    O> omlpsolve("get_mat", "mymodel", 1, 2)
       78.2600
    O> omlpsolve("solve", "mymodel")
         0
    O> omlpsolve("get_objective", "mymodel")
       31.7828
    O> omlpsolve("get_variables", "mymodel")
    {
    28.6
    0
    0
    31.8276
    }

    O> omlpsolve("get_constraints", "mymodel")
    {
    92.3
    6.8640
    391.293
    }

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 O-Matrix routine to get the handle from the model name: get_handle.
For example:

    O> omlpsolve("get_handle", "mymodel")
    0

Don't forget to free the handle and its associated memory when you are done:

    O> omlpsolve("delete_lp", "mymodel")

In the next part of this documentation, the handle is used. But if you name the model, the name could thus also be used.

### Matrices

In O-Matrix, all numerical data is stored in matrices; even a scalar variable. O-Matrix also supports complex numbers. omlpsolve can only work with real numbers. For example:

    O> omlpsolve("add_constraint", lp, [0.24, 0, 11.31, 0], 1, 14.8);

Most of the time, variables are used to provide the data:

    O> omlpsolve("add_constraint", lp, a1, 1, 14.8);

Where a1 is a matrix variable.

Matrices with too few or too much elements gives an 'invalid vector.' error.

Most of the time, omlpsolve needs vectors (rows or columns). In all situations, it doesn't matter if the vectors are row or column vectors. The driver accepts them both. For example:

    O> omlpsolve("add_constraint", lp, {0.24, 0, 11.31, 0}, 1, 14.8);

Which is a column vector, but it is also accepted.

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 O-Matrix 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 O-Matrix matrix.

### Maximum usage of matrices with omlpsolve

Because O-Matrix is all about matrices, all lpsolve API routines that need a column or row number to get/set information for that column/row are extended in the omlpsolve O-Matrix driver to also work with matrices. 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 omlpsolve O-Matrix driver however also allows specifying a vector to set the integer status of all variables at once. The API call is: return = omlpsolve("set_int", lp, column, must_be_int). The matrix version of this call is: return = omlpsolve("set_int", lp, [must_be_int]). The API call to return the integer status of a variable is: return = omlpsolve("is_int", lp, column). The matrix version of this call is: [is_int] = omlpsolve("is_int", lp)
Also note the get_mat and set_mat routines. In O-Matrix these are extended to return/set the complete constraint matrix. See following example.

Above example can thus also be done as follows:
(Note that you can execute this example by entering command per command as shown below or by just entering example2. This will execute example2.oms.)

    O> lp=omlpsolve("make_lp", 0, 4);
    O> omlpsolve("set_verbose", lp, 3);
    O> omlpsolve("set_obj_fn", lp, [1, 3, 6.24, 0.1]);
    O> omlpsolve("add_constraint", lp, [0, 78.26, 0, 2.9], 2, 92.3);
    O> omlpsolve("add_constraint", lp, [0.24, 0, 11.31, 0], 1, 14.8);
    O> omlpsolve("add_constraint", lp, [12.68, 0, 0.08, 0.9], 2, 4);
    O> omlpsolve("set_lowbo", lp, [28.6, 0, 0, 18]);
    O> omlpsolve("set_upbo", lp, [INF, INF, INF, 48.98]);
    O> omlpsolve("set_col_name", lp, {"COLONE", "COLTWO", "COLTHREE", "COLFOUR"});
    O> omlpsolve("set_row_name", lp, {"THISROW", "THATROW", "LASTROW"});
    O> omlpsolve("write_lp", lp, "a.lp");
    O> omlpsolve("get_mat", lp)
    {
    [ 0 , 78.26 , 0 , 2.9 ]
    [ 0.24 , 0 , 11.31 , 0 ]
    [ 12.68 , 0 , 0.08 , 0.9 ]
    }

    O> omlpsolve("solve", lp)
    0
    O> omlpsolve("get_objective", lp)
    31.7828
    O> omlpsolve("get_variables", lp)
    {
    28.6
    0
    0
    31.8276
    }

    O> omlpsolve("get_constraints", lp)
    {
    92.3
    6.8640
    391.293
    }

Note the usage of INF in set_upbo. This stands for "infinity". Meaning an infinite upper bound. It is also possible to use -INF to express minus infinity. This can for example be used to create a free variable.

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:

    O> A=omlpsolve("get_mat", lp);
    O> X=omlpsolve("get_variables", lp);
    O> B = A * X
    O> B
    {
    92.3
    6.864
    391.293
    }

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:

    O> omlpsolve("get_constraints", lp)
    {
    92.3
    6.864
    391.293
    }

Exactly the same as the calculated B vector, as expected.

Also the value of the objective can be calculated in a same way:

    O> C=omlpsolve("get_obj_fn", lp);
    O> X=omlpsolve("get_variables", lp);
    O> obj = C * X
    O> obj
    31.7828

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:

    O> omlpsolve("get_objective", lp)
    31.7828

Again exactly the same as the calculated obj value, as expected.

### oms scripts

O-Matrix can execute a sequence of statements stored in files. Such files are called oms files because they must have the file type of ".oms" as the last part of their filename (extension).

oms scripts can be compared with batch files or scripts. You can put O-Matrix commands in them and execute them at any time. The oms script is executed like any other command, by entering its name (without the .oms extension).

The omlpsolve O-Matrix distribution contains some example oms scripts to demonstrate this.

You can also edit these files with your favourite text editor (or notepad).

#### example1.oms

Contains the commands as shown in the first example of this article. To execute and also see which commands are executed in the debug window, use following commands:

    O> stop
    O> trace on example1.oms
    O> quit
    O> example1

Note however that execution is much slower when trace is on. It is only used here to see the statements executed.

#### example2.oms

Contains the commands as shown in the second example of this article. To execute and also see which commands are executed in the debug window, use following commands:

    O> stop
    O> trace on example2.oms
    O> quit
    O> example2

Note however that execution is much slower when trace is on. It is only used here to see the statements executed.

#### example3.oms

Contains the commands of a practical example. See further in this article.

#### example4.oms

Contains the commands of a practical example. See further in this article.

#### example5.oms

Contains the commands of a practical example. See further in this article.

#### example6.oms

Contains the commands of a practical example. See further in this article.

#### lp_solve.oms

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. See the beginning of the file to see its usage:

     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.

Example of usage. To create and solve following lp-model:

    max: -x1 + 2 x2;
    C1: 2x1 + x2 < 5;
    -4 x1 + 4 x2 <5;

    int x2,x1;

The following command can be used:

    O> include lp_solve.oms
    O> [obj, x]=lp_solve([-1, 2], {[2, 1], [-4, 4]}, [5, 5], [-1, -1], [], [], [1, 2])
    O> obj
    3
    O> x
    {
    1
    2
    }

#### lp_maker.oms

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. See the beginning of the file to see its usage:

     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
              vlb: n vector of non-negative 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.
         setminim: Set maximum lp when this flag equals 0 or omitted.

       OUTPUT: lp_handle is an integer handle to the lp created.

Example of usage. To create following lp-model:

    max: -x1 + 2 x2;
    C1: 2x1 + x2 < 5;
    -4 x1 + 4 x2 <5;

    int x2,x1;

The following command can be used:

    O> include lp_maker.oms
    O> lp=lp_maker([-1, 2], {[2, 1], [-4, 4]}, [5, 5], [-1, -1], [], [], [1, 2])
    O> lp
    0

To solve the model and get the solution:

    O> omlpsolve("solve", lp)
    0
    O> omlpsolve("get_objective", lp)
    3
    O> omlpsolve("get_variables", lp)
    {
    1
    2
    }

Don't forget to free the handle and its associated memory when you are done:

    O> omlpsolve("delete_lp", lp);

#### lpdemo.oms

Contains several examples to build and solve lp models. To execute and also see which commands are executed in the debug window, use following commands:

    O> stop
    O> trace on lpdemo.oms
    O> quit
    O> lpdemo

Note however that execution is much slower when trace is on. It is only used here to see the statements executed.

#### ex.oms

Contains several examples to build and solve lp models. Also solves the lp_examples from the lp_solve distribution. To execute and also see which commands are executed in the debug window, use following commands:

    O> stop
    O> trace on ex.oms
    O> quit
    O> ex

Note however that execution is much slower when trace is on. It is only used here to see the statements executed.

### A practical example

We shall illustrate the method of linear programming by means of a simple example, giving a combination graphical/numerical solution, and then solve both a slightly as well as a substantially more complicated problem.

Suppose a farmer has 75 acres on which to plant two crops: wheat and barley. To produce these crops, it costs the farmer (for seed, fertilizer, etc.) $120 per acre for the wheat and $210 per acre for the barley. The farmer has $15000 available for expenses. But after the harvest, the farmer must store the crops while awaiting favourable market conditions. The farmer has storage space for 4000 bushels. Each acre yields an average of 110 bushels of wheat or 30 bushels of barley. If the net profit per bushel of wheat (after all expenses have been subtracted) is $1.30 and for barley is $2.00, how should the farmer plant the 75 acres to maximize profit?

We begin by formulating the problem mathematically. First we express the objective, that is the profit, and the constraints algebraically, then we graph them, and lastly we arrive at the solution by graphical inspection and a minor arithmetic calculation.

Let x denote the number of acres allotted to wheat and y the number of acres allotted to barley. Then the expression to be maximized, that is the profit, is clearly

P = (110)(1.30)x + (30)(2.00)y = 143x + 60y.

There are three constraint inequalities, specified by the limits on expenses, storage and acreage. They are respectively:

120x + 210y <= 15000
110x + 30y <= 4000
x + y <= 75

Strictly speaking there are two more constraint inequalities forced by the fact that the farmer cannot plant a negative number of acres, namely:

x >= 0, y >= 0.

Next we graph the regions specified by the constraints. The last two say that we only need to consider the first quadrant in the x-y plane. Here's a graph delineating the triangular region in the first quadrant determined by the first inequality.

    O> clear
    O> X = 0.1:0.05:125;
    O> Y1 = (15000. - 120*X)/210;
    O> bar(X, Y1)

Now let's put in the other two constraint inequalities.

    O> clear
    O> X = 0.1:0.05:38;
    O> mlmode
    O> Y1 = (15000. - 120*X)/210;
    O> Y2 = max((4000 - 110.*X)./30, 0);
    O> Y3 = max(75 - X, 0.);
    O> Ytop = min(min(Y1, Y2), Y3);
    O> omatrix
    O> bar(X, Ytop)
    O> gtitle("Solution space")

The black area is the solution space that holds valid solutions. This means that any point in this area fulfils the constraints.

Now let's superimpose on top of this picture a contour plot of the objective function P.

    O> mlmode meshgrid.m
    O> [U, V] = meshgrid(0:1:40, 0:1:80);
    O> Ur = U.row(1)
    O> Vc = V.col(1)
    O> Z = 143.*U + 60.*V
    O> levels = (0:1:11)*1000.
    O> contour(Z', levels, Ur', Vc');
    O> gtitle("Solution space and objective")

The lines give a picture of the objective function. All solutions that intersect with the black area are valid solutions, meaning that this result also fulfils the set constraints. The more the lines go to the right, the higher the objective value is. The optimal solution or best objective is a line that is still in the black area, but with an as large as possible value.

It seems apparent that the maximum value of P will occur on the level curve (that is, level line) that passes through the vertex of the polygon that lies near (22,53).
It is the intersection of x + y = 75 and 110*x + 30*y = 4000
This is a corner point of the diagram. This is not a coincidence. The simplex algorithm, which is used by lp_solve, starts from a theorem that the optimal solution is such a corner point.
In fact we can compute the result:

    O> x = {[1, 1], [110, 30]} \ {75, 4000}
    O> print "x =", x
    x = {
    21.875
    53.125
    }

The acreage that results in the maximum profit is 21.875 for wheat and 53.125 for barley. In that case the profit is:

    O> P = [143, 60] * x
    O> print "Profit, P =", P
    Profit, P = 6315.63

That is, $6315.63.

Note that these command are in script example3.oms

Now, lp_solve comes into the picture to solve this linear programming problem more generally. After that we will use it to solve two more complicated problems involving more variables and constraints.

For this example, we use the higher-level script lp_maker to build the model and then some lp_solve API calls to retrieve the solution. Here is again the usage of lp_maker:

     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
              vlb: n vector of non-negative 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.
         setminim: Set maximum lp when this flag equals 0 or omitted.

       OUTPUT: lp_handle is an integer handle to the lp created.

Now let's formulate this model with lp_solve:

    O> f = [143, 60];
    O> A = {[120, 210], [110, 30], [1, 1]};
    O> b = {15000, 4000, 75};
    O> lp = lp_maker(f, A, b, [-1, -1, -1], [], [], [], 1, 0);
    O> solvestat = omlpsolve("solve", lp)
    O> omlpsolve("get_objective", lp)
    6315.63
    O> omlpsolve("get_variables", lp)
    {
    21.875
    53.125
    }
    O> omlpsolve("delete_lp", lp);

Note that these command are in script example4.oms

With the higher-level script lp_maker, we provide all data to lp_solve. lp_solve returns a handle (lp) to the created model. Then the API call 'solve' is used to calculate the optimal solution of the model. The value of the objective function is retrieved via the API call 'get_objective' and the values of the variables are retrieved via the API call 'get_variables'. At last, the model is removed from memory via a call to 'delete_lp'. Don't forget this to free all memory allocated by lp_solve.

The solution is the same answer we obtained before. Note that the non-negativity constraints are accounted implicitly because variables are by default non-negative in lp_solve.

Well, we could have done this problem by hand (as shown in the introduction) because it is very small and it can be graphically presented.
Now suppose that the farmer is dealing with a third crop, say corn, and that the corresponding data is:

> cost per acre | $150.75
> yield per acre | 125 bushels
> profit per bushel | $1.56

With three variables it is already a lot more difficult to show this model graphically. Adding more variables makes it even impossible because we can't imagine anymore how to represent this. We only have a practical understanding of 3 dimentions, but beyound that it is all very theorethical.

If we denote the number of acres allotted to corn by z, then the objective function becomes:

P = (110)(1.30)x + (30)(2.00)y + (125)(1.56) = 143x + 60y + 195z

And the constraint inequalities are:

120x + 210y + 150.75z <= 15000
110x + 30y + 125z <= 4000
x + y + z <= 75
x >= 0, y >= 0, z >= 0

The problem is solved with lp_solve as follows:

    O> f = [143, 60, 195];
    O> A = {[120, 210, 150.75], [110, 30, 125], [1, 1, 1]};
    O> b = {15000, 4000, 75};
    O> lp = lp_maker(f, A, b, [-1, -1, -1], [], [], [], 1, 0);
    O> solvestat = omlpsolve("solve", lp)
    O> omlpsolve("get_objective", lp)
    6986.84
    O> omlpsolve("get_variables", lp)
    {
    0
    56.5789
    18.4211
    }
    O> omlpsolve("delete_lp", lp);

Note that these command are in script example5.oms

So the farmer should ditch the wheat and plant 56.5789 acres of barley and 18.4211 acres of corn.

There is no practical limit on the number of variables and constraints that O-Matrix can handle. Certainly none that the relatively unsophisticated user will encounter. Indeed, in many true applications of the technique of linear programming, one needs to deal with many variables and constraints. The solution of such a problem by hand is not feasible, and software like O-Matrix is crucial to success. For example, in the farming problem with which we have been working, one could have more crops than two or three. Think agribusiness instead of family farmer. And one could have constraints that arise from other things beside expenses, storage and acreage limitations. For example:

- Availability of seed. This might lead to constraint inequalities like xj < k.
- Personal preferences. Thus the farmer's spouse might have a preference for one variety over another and insist on a corresponding planting, or something similar with a collection of crops; thus constraint inequalities like xi < xj or x1 + x2 > x3.
- Government subsidies. It may take a moment's reflection on the reader's part, but this could lead to inequalities like xj > k.

Below is a sequence of commands that solves exactly such a problem. You should be able to recognize the objective expression and the constraints from the data that is entered. But as an aid, you might answer the following questions:

- How many crops are under consideration?
- What are the corresponding expenses? How much is available for expenses?
- What are the yields in each case? What is the storage capacity?
- How many acres are available?
- What crops are constrained by seed limitations? To what extent?
- What about preferences?
- What are the minimum acreages for each crop?

    O> f = [110*1.3, 30*2.0, 125*1.56, 75*1.8, 95*.95, 100*2.25, 50*1.35];
    O> A = {[120,210,150.75,115,186,140,85],[110,30,125,75,95,100,50],[1,1,1,1,1,1,1],
                      [1,-1,0,0,0,0,0],[0,0,1,0,-2,0,0],[0,0,0,-1,0,-1,1]};
    O> b = {55000, 40000, 400, 0, 0, 0};
    O> lp = lp_maker(f, A, b, [-1,-1,-1,-1,-1,-1],[10,10,10,10,20,20,20],[100,INF,50,INF,INF,250,INF],[],1,0);
    O> solvestat = omlpsolve("solve", lp)
    O> omlpsolve("get_objective", lp)
    75398
    O> omlpsolve("get_variables", lp)
    {
    10
    10
    40
    45.6522
    20
    250
    20
    }
    O> omlpsolve("delete_lp", lp);

Note that these command are in script example6.oms

Note that we have used in this formulation the vlb and vub arguments of lp_maker. This to set lower and upper bounds on variables. This could have been done via extra constraints, but it is more performant to set bounds on variables. Also note that Inf is used for variables that have no upper limit. This stands for Infinity.

Note that despite the complexity of the problem, lp_solve solves it almost instantaneously. It seems the farmer should bet the farm on crop number 6. We strongly suggest you alter the expense and/or the storage limit in the problem and see what effect that has on the answer.

### Another, more theoretical, example

Suppose we want to solve the following linear program using O-Matrix:

max 4x1 + 2x2 + x3
s. t. 2x1 + x2 <= 1
x1 + 2x3 <= 2
x1 + x2 + x3 = 1
x1 >= 0
x1 <= 1
x2 >= 0
x2 <= 1
x3 >= 0
x3 <= 2

Convert the LP into O-Matrix format we get:

f = [4, 2, 1]
A = {[2, 1, 0], [1, 0, 2], [1, 1, 1]}
b = {1, 2, 1}

Note that constraints on single variables are not put in the constraint matrix. lp_solve can set bounds on individual variables and this is more performant than creating additional constraints. These bounds are:

l = [ 0, 0, 0]
u = [ 1, 1, 2]

Now lets enter this in O-Matrix:

    O> f = [4, 2, 1];
    O> A = {[2, 1, 0], [1, 0, 2], [1, 1, 1]};
    O> b = {1, 2, 1};
    O> l = [ 0, 0, 0];
    O> u = [ 1, 1, 2];

Now solve the linear program using O-Matrix: Type the commands

    O> lp = lp_maker(f, A, b, [-1, -1, -1], l, u, [], 1, 0);
    O> solvestat = omlpsolve("solve", lp)
    O> omlpsolve("get_objective", lp)
    2.5
    O> omlpsolve("get_variables", lp)
    {
    0.5
    0
    0.5
    }
    O> omlpsolve("delete_lp", lp)

What to do when some of the variables are missing ?
For example, suppose there are no lower bounds on the variables. In this case define l to be the empty set using the O-Matrix command:

    O> l = [];

This has the same effect as before, because lp_solve has as default lower bound for variables 0.

But what if you want that variables may also become negative?
Then you can use -INF as lower bounds:

    O> l = [-INF, -INF, -INF];

Solve this and you get a different result:

    O> lp = lp_maker(f, A, b, [-1, -1, -1], l, u, [], 1, 0);
    O> solvestat = omlpsolve("solve", lp)
    O> omlpsolve("get_objective", lp)
    2.66667
    O> omlpsolve("get_variables", lp)
    {
    0.666667
    -0.333333
    0.666667
    }
    O> omlpsolve("delete_lp", lp)

### Overview of API routines

Note that everwhere where lp is used as argument that this can be a handle (lp_handle) or the models name.

- add_column, add_columnex
  - return = omlpsolve("add_column", lp, [column])
  - return = omlpsolve("add_columnex", lp, [column])
  - Both have the same interface from add_column but act as add_columnex
- add_constraint, add_constraintex
  - return = omlpsolve("add_constraint", lp, [row], constr_type, rh)
  - return = omlpsolve("add_constraintex", lp, [row], constr_type, rh)
  - Both have the same interface from add_constraint but act as add_constraintex
- add_SOS
  - return = omlpsolve("add_SOS", lp, name, sostype, priority, [sosvars], [weights])
  - The count argument in the API documentation is not needed in O-Matrix since the number of elements is derived from the size of the sosvars and weights matrices. These must have the same size.
- column_in_lp
  - return = omlpsolve("column_in_lp", lp, [column])
  - No special considerations.
- copy_lp
  - lp_handle = omlpsolve("copy_lp", lp)
  - No special considerations.
- default_basis
  - omlpsolve("default_basis", lp)
  - No special considerations.
- del_column
  - return = omlpsolve("del_column", lp, column)
  - No special considerations.
- del_constraint
  - return = omlpsolve("del_constraint", lp, del_row)
  - No special considerations.
- delete_lp
  - omlpsolve("delete_lp", lp)
  - No special considerations.
- free_lp
  - omlpsolve("free_lp", lp)
  - lp is not changed as in the lpsolve API since it is a read_only input parameter. So it acts the same as delete_lp.
- get_anti_degen
  - return = omlpsolve("get_anti_degen", lp)
  - No special considerations.
- get_basis
  - [bascolumn] = omlpsolve("get_basis", lp {, nonbasic})
  - The bascolumn argument in the API documentation is here the return value. The nonbasic argument is optional in O-Matrix. If not provided, then 0 is used.
- get_basiscrash
  - return = omlpsolve("get_basiscrash", lp)
  - No special considerations.
- get_bb_depthlimit
  - return = omlpsolve("get_bb_depthlimit", lp)
  - No special considerations.
- get_bb_floorfirst
  - return = omlpsolve("get_bb_floorfirst", lp)
  - No special considerations.
- get_bb_rule
  - return = omlpsolve("get_bb_rule", lp)
  - No special considerations.
- get_bounds_tighter
  - return = omlpsolve("get_bounds_tighter", lp)
  - No special considerations.
- get_break_at_value
  - return = omlpsolve("get_break_at_value", lp)
  - No special considerations.
- get_col_name
  - name = omlpsolve("get_col_name", lp, column)
  - [names] = omlpsolve("get_col_name", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_column get_columnex
  - [column, return] = omlpsolve("get_column", lp, col_nr)
  - [column, return] = omlpsolve("get_columnex", lp, col_nr)
  - The column argument in the API documentation is here the first return value.
  - The return code of the call is the second return value.
- get_constr_type
  - return = omlpsolve("get_constr_type", lp, row)
  - [constr_type] = omlpsolve("get_constr_type", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_constr_value
  - return = omlpsolve("get_constr_value", lp, row {, primsolution})
  - The primsolution argument is optional. If not provided, then the solution of last solve is used.
- get_constraints
  - [constr, return] = omlpsolve("get_constraints", lp)
  - The constr argument in the API documentation is here the first return value.
  - The return code of the call is the second return value.
- get_dual_solution
  - [duals, return] = omlpsolve("get_dual_solution", lp)
  - The duals argument in the API documentation is here the first return value.
  - In the API, element 0 is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
  - The return code of the call is the second return value.
- get_epsb
  - return = omlpsolve("get_epsb", lp)
  - No special considerations.
- get_epsd
  - return = omlpsolve("get_epsd", lp)
  - No special considerations.
- get_epsel
  - return = omlpsolve("get_epsel", lp)
  - No special considerations.
- get_epsint
  - return = omlpsolve("get_epsint", lp)
  - No special considerations.
- get_epsperturb
  - return = omlpsolve("get_epsperturb", lp)
  - No special considerations.
- get_epspivot
  - return = omlpsolve("get_epspivot", lp)
  - No special considerations.
- get_improve
  - return = omlpsolve("get_improve", lp)
  - No special considerations.
- get_infinite
  - return = omlpsolve("get_infinite", lp)
  - No special considerations.
- get_lowbo
  - return = omlpsolve("get_lowbo", lp, column)
  - [return] = omlpsolve("get_lowbo", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_lp_index
  - return = omlpsolve("get_lp_index", lp, orig_index)
  - No special considerations.
- get_lp_name
  - name = omlpsolve("get_lp_name", lp)
  - No special considerations.
- get_mat
  - value = omlpsolve("get_mat", lp, row, col)
  - [matrix, return] = omlpsolve("get_mat", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix in the first return value. The return code of the call is the second return value.
- get_max_level
  - return = omlpsolve("get_max_level", lp)
  - No special considerations.
- get_maxpivot
  - return = omlpsolve("get_maxpivot", lp)
  - No special considerations.
- get_mip_gap
  - return = omlpsolve("get_mip_gap", lp, absolute)
  - No special considerations.
- get_nameindex
  - return = omlpsolve("get_nameindex", lp, name, isrow)
  - No special considerations.
- get_Ncolumns
  - return = omlpsolve("get_Ncolumns", lp)
  - No special considerations.
- get_negrange
  - return = omlpsolve("get_negrange", lp)
  - No special considerations.
- get_nonzeros
  - return = omlpsolve("get_nonzeros", lp)
  - No special considerations.
- get_Norig_columns
  - return = omlpsolve("get_Norig_columns", lp)
  - No special considerations.
- get_Norig_rows
  - return = omlpsolve("get_Norig_rows", lp)
  - No special considerations.
- get_Nrows
  - return = omlpsolve("get_Nrows", lp)
  - No special considerations.
- get_obj_bound
  - return = omlpsolve("get_obj_bound", lp)
  - No special considerations.
- get_objective
  - return = omlpsolve("get_objective", lp)
  - No special considerations.
- get_orig_index
  - return = omlpsolve("get_orig_index", lp, lp_index)
  - No special considerations.
- get_origcol_name
  - name = omlpsolve("get_origcol_name", lp, column)
  - [names] = omlpsolve("get_origcol_name", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_origrow_name
  - name = omlpsolve("get_origrow_name", lp, row)
  - [names] = omlpsolve("get_origrow_name", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_pivoting
  - return = omlpsolve("get_pivoting", lp)
  - No special considerations.
- get_presolve
  - return = omlpsolve("get_presolve", lp)
  - No special considerations.
- get_presolveloops
  - return = omlpsolve("get_presolveloops", lp)
  - No special considerations.
- get_primal_solution
  - [pv, return] = omlpsolve("get_primal_solution", lp)
  - The pv argument in the API documentation is here the first return value.
  - The return code of the call is the second return value.
- get_print_sol
  - return = omlpsolve("get_print_sol", lp)
  - No special considerations.
- get_ptr_constraints
  - Not implemented.
- get_ptr_dualsolution
  - Not implemented.
- get_ptr_primal_solution
  - Not implemented.
- get_ptr_sensitivity_obj, get_ptr_sensitivity_objex
  - Not implemented.
- get_ptr_sensitivity_rhs
  - Not implemented.
- get_ptr_variables
  - Not implemented.
- get_rh
  - return = omlpsolve("get_rh", lp, row)
  - [rh] = omlpsolve("get_rh", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_rh_range
  - return = omlpsolve("get_rh_range", lp, row)
  - [rh_ranges] = omlpsolve("get_rh_range", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_row get_rowex
  - [row, return] = omlpsolve("get_row", lp, row_nr)
  - [row, return] = omlpsolve("get_rowex", lp, row_nr)
  - The row argument in the API documentation is here the first return value.
  - In the API, element 0 is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
  - The return code of the call is the second return value.
- get_row_name
  - name = omlpsolve("get_row_name", lp, row)
  - [names] = omlpsolve("get_row_name", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_scalelimit
  - return = omlpsolve("get_scalelimit", lp)
  - No special considerations.
- get_scaling
  - return = omlpsolve("get_scaling", lp)
  - No special considerations.
- get_sensitivity_obj, get_sensitivity_objex
  - [objfrom, objtill, objfromvalue, objtillvalue, return] = omlpsolve("get_sensitivity_obj", lp)
  - [objfrom, objtill, objfromvalue, objtillvalue, return] = omlpsolve("get_sensitivity_objex", lp)
  - The objfrom, objtill, objfromvalue, objtillvalue arguments in the API documentation are here the return values. Note that O-Matrix allows the return of fewer variables. For example if only objfrom and objtill are needed then the call can be [objfrom, objtill] = omlpsolve("get_sensitivity_obj", lp). The unrequested values are even not calculated.
  - Since the API routine doesn't calculate the objtillvalue value at this time, O-Matrix always returns a zero vector for this.
  - The return code of the call is the last value.
  - get_sensitivity_obj and get_sensitivity_objex are both implemented, but have the same functionality.
- get_sensitivity_rhs, get_sensitivity_rhsex
  - [duals, dualsfrom, dualstill, return] = omlpsolve("get_sensitivity_rhs", lp)
  - [duals, dualsfrom, dualstill, return] = omlpsolve("get_sensitivity_rhsex", lp)
  - The duals, dualsfrom, dualstill arguments in the API documentation are here the return values. Note that O-Matrix allows the return of fewer variables. For example if only duals is needed then the call can be [duals] = omlpsolve("get_sensitivity_rhs", lp). The unrequested values are even not calculated.
  - The return code of the call is the last value.
  - get_sensitivity_rhs and get_sensitivity_rhsex are both implemented, but have the same functionality.
- get_simplextype
  - return = omlpsolve("get_simplextype", lp)
  - No special considerations.
- get_solutioncount
  - return = omlpsolve("get_solutioncount", lp)
  - No special considerations.
- get_solutionlimit
  - return = omlpsolve("get_solutionlimit", lp)
  - No special considerations.
- get_status
  - return = omlpsolve("get_status", lp)
  - No special considerations.
- get_statustext
  - return = omlpsolve("get_statustext", lp, statuscode)
  - No special considerations.
- get_timeout
  - return = omlpsolve("get_timeout", lp)
  - No special considerations.
- get_total_iter
  - return = omlpsolve("get_total_iter", lp)
  - No special considerations.
- get_total_nodes
  - return = omlpsolve("get_total_nodes", lp)
  - No special considerations.
- get_upbo
  - return = omlpsolve("get_upbo", lp, column)
  - [upbo] = omlpsolve("get_upbo", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_var_branch
  - return = omlpsolve("get_var_branch", lp, column)
  - [var_branch] = omlpsolve("get_var_branch", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_var_dualresult
  - return = omlpsolve("get_var_dualresult", lp, index)
  - No special considerations.
- get_var_primalresult
  - return = omlpsolve("get_var_primalresult", lp, index)
  - No special considerations.
- get_var_priority
  - return = omlpsolve("get_var_priority", lp, column)
  - [var_priority] = omlpsolve("get_var_priority", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- get_variables
  - [var, return] = omlpsolve("get_variables", lp)
  - The var argument in the API documentation is here the first return value.
  - The return code of the call is the second return value.
- get_verbose
  - return = omlpsolve("get_verbose", lp)
  - No special considerations.
- get_working_objective
  - return = omlpsolve("get_working_objective", lp)
  - No special considerations.
- guess_basis
  - [basisvector, return] = omlpsolve("guess_basis", lp, [guessvector])
  - In the API, element 0 of guessvector is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
  - In the API, element 0 of basisvector is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
- has_BFP
  - return = omlpsolve("has_BFP", lp)
  - No special considerations.
- has_XLI
  - return = omlpsolve("has_XLI", lp)
  - No special considerations.
- is_add_rowmode
  - return = omlpsolve("is_add_rowmode", lp)
  - No special considerations.
- is_anti_degen
  - return = omlpsolve("is_anti_degen", lp, testmask)
  - No special considerations.
- is_binary
  - return = omlpsolve("is_binary", lp, column)
  - [binary] = omlpsolve("is_binary", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- is_break_at_first
  - return = omlpsolve("is_break_at_first", lp)
  - No special considerations.
- is_constr_type
  - return = omlpsolve("is_constr_type", lp, row, mask)
  - No special considerations.
- is_debug
  - return = omlpsolve("is_debug", lp)
  - No special considerations.
- is_feasible
  - return = omlpsolve("is_feasible", lp, [values] {, threshold})
  - The threshold argument is optional. When not provided, the value of get_epsint will be taken.
- is_free is_unbounded
  - return = omlpsolve("is_free", lp, column)
  - return = omlpsolve("is_unbounded", lp, column)
  - [free] = omlpsolve("is_free", lp)
  - [free] = omlpsolve("is_unbounded", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- is_infinite
  - return = omlpsolve("is_infinite", lp, value)
  - No special considerations.
- is_int
  - return = omlpsolve("is_int", lp, column)
  - [int] = omlpsolve("is_int", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- is_integerscaling
  - return = omlpsolve("is_integerscaling", lp)
  - No special considerations.
- is_maxim
  - return = omlpsolve("is_maxim", lp)
  - No special considerations.
- is_nativeBFP
  - return = omlpsolve("is_nativeBFP", lp)
  - No special considerations.
- is_nativeXLI
  - return = omlpsolve("is_nativeXLI", lp)
  - No special considerations.
- is_negative
  - return = omlpsolve("is_negative", lp, column)
  - [negative] = omlpsolve("is_negative", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- is_piv_mode
  - return = omlpsolve("is_piv_mode", lp, testmask)
  - No special considerations.
- is_piv_rule
  - return = omlpsolve("is_piv_rule", lp, rule)
  - No special considerations.
- is_presolve
  - return = omlpsolve("is_presolve", lp, testmask)
  - No special considerations.
- is_scalemode
  - return = omlpsolve("is_scalemode", lp, testmask)
  - No special considerations.
- is_scaletype
  - return = omlpsolve("is_scaletype", lp, scaletype)
  - No special considerations.
- is_semicont
  - return = omlpsolve("is_semicont", lp, column)
  - [semicont] = omlpsolve("is_semicont", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- is_SOS_var
  - return = omlpsolve("is_SOS_var", lp, column)
  - [SOS_var] = omlpsolve("is_SOS_var", lp)
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows retrieving the values into a O-Matrix matrix.
- is_trace
  - return = omlpsolve("is_trace", lp)
  - No special considerations.
- is_use_names
  - return = omlpsolve("is_use_names", lp, isrow)
  - No special considerations.
- lp_solve_version
  - versionstring = omlpsolve("lp_solve_version")
  - The omlpsolve API routine returns the version information in 4 provided argument variables while the O-Matrix version returns the information as a string in the format major.minor.release.build
- make_lp
  - lp_handle = omlpsolve("make_lp", rows, columns)
  - lp_handle is not a pointer to an lprec structure as in the API, but an incrementing handle number starting from 0.
- print_constraints
  - omlpsolve("print_constraints", lp {, columns})
  - columns is optional. If not specified, then 1 is used.
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
  - The same information can also be obtained via omlpsolve("get_constraints", lp). This shows the result on screen.
- print_debugdump
  - return = omlpsolve("print_debugdump", lp, filename)
  - No special considerations.
- print_duals
  - omlpsolve("print_duals", lp)
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
  - The same information can be obtained via omlpsolve("get_dual_solution", lp). This shows the result on screen.
- print_lp
  - omlpsolve("print_lp", lp)
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
- print_objective
  - omlpsolve("print_objective", lp)
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
  - The same information can be obtained via omlpsolve("get_objective", lp). This shows the result on screen.
- print_scales
  - omlpsolve("print_scales", lp)
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
- print_solution
  - omlpsolve("print_solution", lp {, columns})
  - columns is optional. If not specified, then 1 is used.
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
  - The same information can also be obtained via omlpsolve("get_variables", lp). This shows the result on screen.
- print_str
  - omlpsolve("print_str", lp, str)
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
- print_tableau
  - omlpsolve("print_tableau", lp)
  - First call set_outputfile to specify where the information is written to. In the API documentation it is written that by default, the output goes to stdout, but under O-Matrix (Windows) this means that the output is not shown.
- put_abortfunc
  - Not implemented.
- put_logfunc
  - Not implemented.
  - However, the omlpsolve driver sets a log function to redirect the output of lpsolve from stdout (which is not visible in Windows O-Matrix) to the command window of O-Matrix. As such, all reported output can be seen in O-Matrix. How much output is seen is controlled by the verbose level that can be defined by set_verbose or can be specified in the read_ routines. Note that at least O-Matrix version 5.8 is needed to see this information on the command window. Older versions will not print information on the command window.
- put_msgfunc
  - Not implemented.
- read_basis
  - [ret, info] = omlpsolve("read_basis", lp, filename)
  - No special considerations.
- read_freemps, read_freeMPS
  - lp_handle = omlpsolve("read_freemps", filename {, verbose})
  - lp_handle = omlpsolve("read_freeMPS", filename {, verbose})
  - In the lpsolve API, read_freemps needs a FILE handle. In O-Matrix it needs the filename and thus acts the same as read_freeMPS.
  - lp_handle is not a pointer to an lprec structure as in the API, but an incrementing handle number starting from 0.
  - verbose is optional. If not specified, then NORMAL is used.
- read_lp, read_LP
  - lp_handle = omlpsolve("read_lp", filename {, verbose {, lp_name}})
  - lp = omlpsolve("read_LP", filename {, verbose {, lp_name}})
  - In the lpsolve API, read_lp needs a FILE handle. In O-Matrix it needs the filename and thus acts the same as read_LP.
  - lp_handle is not a pointer to an lprec structure as in the API, but an incrementing handle number starting from 0.
  - verbose is optional. If not provided then NORMAL is used.
  - lp_name is optional. If not provided then no name is given to the model ("").
- read_mps, read_MPS
  - lp_handle = omlpsolve("read_mps", filename {, verbose})
  - lp_handle = omlpsolve("read_MPS", filename {, verbose})
  - In the lpsolve API, read_mps needs a FILE handle. In O-Matrix it needs the filename and thus acts the same as read_MPS.
  - lp_handle is not a pointer to an lprec structure as in the API, but an incrementing handle number starting from 0.
  - verbose is optional. If not specified, then NORMAL is used.
- read_params
  - return = omlpsolve("read_params", lp, filename {, options })
  - options is optional.
- read_XLI
  - lp_handle = omlpsolve("read_XLI", xliname, modelname {, dataname {, options {, verbose}}}
  - lp_handle is not a pointer to an lprec structure as in the API, but an incrementing handle number starting from 0.
  - dataname is optional. When not provided, "" (NULL) is taken. "" is taken as NULL.
  - options is optional. When not provided, "" is taken.
  - verbose is optional. If not specified, then NORMAL is used.
- reset_basis
  - Not implemented.
  - Use default_basis
- set_basisvar
  - omlpsolve("set_basisvar", lp, basisPos, enteringCol)
  - No special considerations.
- set_add_rowmode
  - return = omlpsolve("set_add_rowmode", lp, turnon)
  - No special considerations.
- set_anti_degen
  - omlpsolve("set_anti_degen", lp, anti_degen)
  - No special considerations.
- set_basis
  - return = omlpsolve("set_basis", lp, [bascolumn], nonbasic)
  - In the API, element 0 of bascolumn is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
- set_basiscrash
  - omlpsolve("set_basiscrash", lp, mode)
  - No special considerations.
- set_bb_depthlimit
  - omlpsolve("set_bb_depthlimit", lp, bb_maxlevel)
  - No special considerations.
- set_bb_floorfirst
  - omlpsolve("set_bb_floorfirst", lp, bb_floorfirst)
  - No special considerations.
- set_bb_rule
  - omlpsolve("set_bb_rule", lp, bb_rule)
  - No special considerations.
- set_BFP
  - return = omlpsolve("set_BFP", lp, filename)
  - No special considerations.
- set_binary
  - return = omlpsolve("set_binary", lp, column, must_be_bin)
  - return = omlpsolve("set_binary", lp, [must_be_bin])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_bounds
  - return = omlpsolve("set_bounds", lp, column, lower, upper)
  - return = omlpsolve("set_bounds", lp, [lower], [upper])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_bounds_tighter
  - omlpsolve("set_bounds_tighter", lp, tighten)
  - No special considerations.
- set_break_at_first
  - omlpsolve("set_break_at_first", lp, break_at_first)
  - No special considerations.
- set_break_at_value
  - omlpsolve("set_break_at_value", lp, break_at_value)
  - No special considerations.
- set_col_name
  - return = omlpsolve("set_col_name", lp, column, name)
  - return = omlpsolve("set_col_name", lp, [names])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_column, set_columnex
  - return = omlpsolve("set_column", lp, col_no, [column])
  - return = omlpsolve("set_columnex", lp, col_no, [column])
  - Both have the same interface from set_column but act as set_columnex
- set_constr_type
  - return = omlpsolve("set_constr_type", lp, row, con_type)
  - return = omlpsolve("set_constr_type", lp, [con_type])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all rows.
- set_debug
  - omlpsolve("set_debug", lp, debug)
  - No special considerations.
- set_epsb
  - omlpsolve("set_epsb", lp, epsb)
  - No special considerations.
- set_epsd
  - omlpsolve("set_epsd", lp, epsd)
  - No special considerations.
- set_epsel
  - omlpsolve("set_epsel", lp, epsel)
  - No special considerations.
- set_epsint
  - omlpsolve("set_epsint", lp, epsint)
  - No special considerations.
- set_epslevel
  - omlpsolve("set_epslevel", lp, epslevel)
  - No special considerations.
- set_epsperturb
  - omlpsolve("set_epsperturb", lp, epsperturb)
  - No special considerations.
- set_epspivot
  - omlpsolve("set_epspivot", lp, epspivot)
  - No special considerations.
- set_free set_unbounded
  - return = omlpsolve("set_free", lp, column)
  - return = omlpsolve("set_unbounded", lp, column)
  - No special considerations.
- set_improve
  - omlpsolve("set_improve", lp, improve)
  - No special considerations.
- set_infinite
  - omlpsolve("set_infinite", lp, infinite)
  - No special considerations.
- set_int
  - return = omlpsolve("set_int", lp, column, must_be_int)
  - return = omlpsolve("set_int", lp, [must_be_int])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_lowbo
  - return = omlpsolve("set_lowbo", lp, column, value)
  - return = omlpsolve("set_lowbo", lp, [values])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_lp_name
  - return = omlpsolve("set_lp_name", lp, name)
  - In O-Matrix, when you name a model, this name can be used everywhere where lp is specified. This to access the model via the name instead of via a handle.
- set_mat
  - return = omlpsolve("set_mat", lp, row, column, value)
  - return = omlpsolve("set_mat", lp, [matrix])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows to set the whole matrix (all rows/columns) at once. This is the most performant way to provide the constraint matrix. The matrix must be two-dimentional.
- set_maxim
  - omlpsolve("set_maxim", lp)
  - No special considerations.
- set_maxpivot
  - omlpsolve("set_maxpivot", max_num_inv)
  - No special considerations.
- set_minim
  - omlpsolve("set_minim", lp)
  - No special considerations.
- set_mip_gap
  - omlpsolve("set_mip_gap", lp, absolute, mip_gap)
  - No special considerations.
- set_negrange
  - omlpsolve("set_negrange", negrange)
  - No special considerations.
- set_obj
  - return = omlpsolve("set_obj", lp, column, value)
  - return = omlpsolve("set_obj", lp, [values])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables. It is then the same as set_obj_fn
- set_obj_bound
  - omlpsolve("set_obj_bound", lp, obj_bound)
  - No special considerations.
- set_obj_fn, set_obj_fnex
  - return = omlpsolve("set_obj_fn", lp, [row])
  - return = omlpsolve("set_obj_fnex", lp, [row])
  - Both have the same interface from set_obj_fn but act as set_obj_fnex
  - In the API, element 0 is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
- set_outputfile
  - return = omlpsolve("set_outputfile", lp, filename)
  - In the API description it says that setting filename to NULL results in writing output back to stdout. In O-Matrix under Windows, output to stdout it not shown. However it results in closing the file. Use "" to have the effect of NULL.
- set_outputstream
  - Not implemented.
- set_pivoting
  - omlpsolve("set_pivoting", lp, pivoting)
  - No special considerations.
- set_preferdual
  - omlpsolve("set_preferdual", lp, dodual)
  - No special considerations.
- set_presolve
  - omlpsolve("set_presolve", lp, do_presolve {, maxloops})
  - The maxloops argument is optional in O-Matrix. If not provided, then infinite is used.
- set_print_sol
  - omlpsolve("set_print_sol", lp, print_sol)
  - No special considerations.
- set_rh
  - return = omlpsolve("set_rh", lp, row, value)
  - return = omlpsolve("set_rh", lp, [values])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all rows. Note that in this case, the value of row 0 is not specified in the matrix.
- set_rh_range
  - return = omlpsolve("set_rh_range", lp, row, deltavalue)
  - return = omlpsolve("set_rh_range", lp, [deltavalues])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all rows.
- set_rh_vec
  - omlpsolve("set_rh_vec", lp, [rh])
  - In the API, element 0 is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
- set_row, set_rowex
  - return = omlpsolve("set_row", lp, row_no, [row])
  - return = omlpsolve("set_rowex", lp, row_no, [row])
  - Both have the same interface from set_row but act as set_rowex
  - In the API, element 0 is not used and values start from element 1. In O-Matrix, there is no unused element in the matrix.
- set_row_name
  - return = omlpsolve("set_row_name", lp, row, name)
  - return = omlpsolve("set_row_name", lp, [names])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all rows.
- set_scalelimit
  - omlpsolve("set_scalelimit", lp, scalelimit)
  - No special considerations.
- set_scaling
  - omlpsolve("set_scaling", lp, scalemode)
  - No special considerations.
- set_semicont
  - return = omlpsolve("set_semicont", lp, column, must_be_sc)
  - return = omlpsolve("set_semicont", lp, [must_be_sc])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_sense
  - omlpsolve("set_sense", lp, maximize)
  - No special considerations.
- set_simplextype
  - omlpsolve("set_simplextype", lp, simplextype)
  - No special considerations.
- set_solutionlimit
  - omlpsolve("set_solutionlimit", lp, simplextype)
  - No special considerations.
- set_timeout
  - omlpsolve("set_timeout", lp, sectimeout)
  - No special considerations.
- set_trace
  - omlpsolve("set_trace", lp, trace)
  - No special considerations.
- set_upbo
  - return = omlpsolve("set_upbo", lp, column, value)
  - return = omlpsolve("set_upbo", lp, [values])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_use_names
  - omlpsolve("set_use_names", lp, isrow, use_names)
  - No special considerations.
- set_var_branch
  - return = omlpsolve("set_var_branch", lp, column, branch_mode)
  - return = omlpsolve("set_var_branch", lp, [branch_mode])
  - In O-Matrix, this routine has two formats. The first format is identical to the API. The second format allows setting a matrix of all variables.
- set_var_weights
  - return = omlpsolve("set_var_weights", lp, [weights])
  - No special considerations.
- set_verbose
  - omlpsolve("set_verbose", lp, verbose)
  - No special considerations.
- set_XLI
  - return = omlpsolve("set_XLI", lp, filename)
  - No special considerations.
- solve
  - result = omlpsolve("solve", lp)
  - No special considerations.
- str_add_column
  - Not implemented.
- str_add_constraint
  - Not implemented.
- str_set_obj_fn
  - Not implemented.
- str_set_rh_vec
  - Not implemented.
- time_elapsed
  - return = omlpsolve("time_elapsed", lp)
  - No special considerations.
- unscale
  - omlpsolve("unscale", lp)
  - No special considerations.
- write_basis
  - omlpsolve("write_basis", lp, filename)
  - No special considerations.
- write_freemps, write_freeMPS
  - return = omlpsolve("write_freemps", lp, filename)
  - return = omlpsolve("write_freeMPS", lp, filename)
  - In the lpsolve API, write_freeMPS needs a FILE handle. In O-Matrix it needs the filename and thus acts the same as write_freemps.
- write_lp, write_LP
  - return = omlpsolve("write_lp", lp, filename)
  - return = omlpsolve("write_LP", lp, filename)
  - In the lpsolve API, write_LP needs a FILE handle. In O-Matrix it needs the filename and thus acts the same as write_lp.
- write_mps, write_MPS
  - return = omlpsolve("write_mps", lp, filename)
  - return = omlpsolve("write_MPS", lp, filename)
  - In the lpsolve API, write_MPS needs a FILE handle. In O-Matrix it needs the filename and thus acts the same as write_mps.
  - No special considerations.
- write_XLI
  - return = omlpsolve("write_XLI", lp, filename {, options {, results}})
  - No special considerations.

### Extra O-Matrix routines

These routines are not part of the lpsolve API, but are added for backwards compatibility. Most of them exist in the lpsolve API with another name.

- [names] = omlpsolve("get_col_names", lp)
  - The same as get_col_name. Implemented for backwards compatibility.
- [constr_type] = omlpsolve("get_constr_types", lp)
  - The same as get_constr_type. Implemented for backwards compatibility.
- [int] = omlpsolve("get_int", lp)
  - The same as is_int. Implemented for backwards compatibility.
- return = omlpsolve("get_no_cols", lp)
  - The same as get_Ncolumns. Implemented for backwards compatibility.
- return = omlpsolve("get_no_rows", lp)
  - The same as get_Nrows. Implemented for backwards compatibility.
- name = omlpsolve("get_objective_name", lp)
  - The same as get_row_name with row=0. Implemented for backwards compatibility.
- [row_vec, return] = omlpsolve("get_obj_fn", lp)
  [row_vec, return] = omlpsolve("get_obj_fun", lp)
  - The same as get_row with row 0. Implemented for backwards compatibility.
- name = omlpsolve("get_problem_name", lp)
  - The same as get_lp_name. Implemented for backwards compatibility.
- [costs] = omlpsolve("get_reduced_costs", lp)
  - The same as get_dual_solution. Implemented for backwards compatibility.
- [names] = omlpsolve("get_row_names", lp)
  - The same as get_row_name. Implemented for backwards compatibility.
- [obj, x, duals, return] = omlpsolve("get_solution", lp)
  - Returns the value of the objective function, the values of the variables and the duals. Implemented for backwards compatibility.
  - The return code of the call is the last value.
- value = omlpsolve("mat_elm", lp)
  - The same as get_mat. Implemented for backwards compatibility.
- [handle_vec] = omlpsolve("print_handle")
  - Returns a vector with open handles. Can be handy to see which handles aren't closed yet with delete_lp or free_lp.
- lp_handle = omlpsolve("read_lp_file", filename {, verbose {, lp_name}})
  - The same as read_LP. Implemented for backwards compatibility.
- lp_handle = omlpsolve("get_handle", lp_name)
  - Get the handle for this model from the models name. If an unknown model name is given (or already deleted), -1 is returned.

### Compile the omlpsolve driver

#### Windows

Under Windows, the omlpsolve O-Matrix driver is a dll: omlpsolve.dll
This dll is an interface to the lpsolve55.dll lpsolve dll that contains the implementation of lp_solve. lpsolve55.dll is distributed with the lp_solve package (archive lp_solve_5.5.0.14_dev.zip). The omlpsolve O-Matrix driver dll (omlpsolve.dll) is just a wrapper between O-Matrix and lp_solve to translate the input/output to/from O-Matrix and the lp_solve library.

The omlpsolve O-Matrix driver is written in C. To compile this code, Microsoft compiler is needed. Other compilers might also work, but this is untested. To make the compilation process easier, a batch file can be used: cvc.bat
It may be necessary to edit this file first to change the path where lp_solve and the O-Matrix dll sources are installed. Change at the beginning lpsolvepath and dllsrcpath. dllsrcpath must point to the folder where dll.h is located.
To make for release, just enter cvc and everything is build.
This compiles three source files: lpsolve.c, omatrix.c and hash.c
Then these are linked with the library lpsolve55.lib to generate the omlpsolve.dll file.
The optional arguments to cvc are used for development. Source files can be provided and then only these are compiled. For example hash.c should only be compiled once while developing. So specifying lpsolve.c as first argument will only compile this file and then link everything. This makes the build process a bit faster. Also the option -DDEMO can be added to add the demo command to test some functionality of lpsolve. This is also only for debugging. Also the option -DDEBUG can be added. This to print some debug information while executing omlpsolve. Should only be used for debugging purposes.

Note that the omlpsolve.dll file can be locked by O-Matrix. Then the build process will fail because the dll can not be overwritten. This can be solved by giving the clear command in O-Matrix. This will free the dll.

#### Unix/Linux

At this moment, there is no O-Matrix version for this platform.

See also Using lpsolve from MATLAB, Using lpsolve from Scilab, Using lpsolve from Octave, Using lpsolve from Python, Using lpsolve from PHP, Using lpsolve from R