# Using lpsolve from Octave

### Octave?

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and non-linear problems numerically, and for performing other numerical experiments. It may also be used as a batch-oriented language.

GNU Octave is also freely redistributable software.

We will not discuss the specifics of Octave here but instead refer the reader to the Octave website and GNU Octave Repository.

### Octave and lpsolve

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

Note that your version of Octave must support dynamic linking. To find out if it does, type the command:

    octave_config_info ("ENABLE_DYNAMIC_LINKING")

at the Octave prompt. Support for dynamic linking is included if this expression returns the string "true".

If this is not the case, then Octave is not able to call dynamic linked routines and as such also not lpsolve. In that case you must recompile Octave with dynamic linked routines enabled. Under Linux, the following commands must be executed for this:

    configure --enable-shared
    make

See Installing Octave for more information.

Under Windows, dynamic linking should already be active. If not, then Octave must be recompiled. The following document can help in this process: README.Windows

The octave dynamic linked routine is in a file with extension .oct. It is impossible to provide a precompiled octlpsolve.oct file with the lpsolve distribution because the structure of the .oct files change often on new releases of Octave and are not compatible with each other. Therefore you must build the driver yourself. Look at the end of this document how to do this.

### Installation

A driver program is needed: octlpsolve (octlpsolve.oct). This driver must be put in a directory known to Octave (in one of the directories from the Octave 'path' command) and Octave can call the octlpsolve solver.

This driver calls lpsolve via the lpsolve shared library (lpsolve55.dll under Windows and liblpsolve55.so under Unix/Linux) (in archives lp_solve_5.5.0.14_dev.zip/lp_solve_5.5.0.14_dev.tar.gz). This has the advantage that the octlpsolve driver doesn't have to be recompiled when an update of lpsolve is provided.

So note the difference between the Octave lpsolve driver that is called octlpsolve and the lpsolve library that implements the API that is called lpsolve55.

There are also some Octave script files (.m) as a quick start.

To test if everything is installed correctly, enter octlpsolve in the Octave command window. If it gives the following, then everything is ok:

    octlpsolve  Octave Interface version 5.5.0.6
    using lpsolve version 5.5.0.14

    Usage: [ret1, ret2, ...] = octlpsolve('functionname', arg1, arg2, ...)

However, if you get the following:

    error: 'octlpsolve' undefined near line 2 column 1

Then Octave cannot find octlpsolve.oct

If you get the following:

    error: Failed to initialise lpsolve library.

Then Octave can find the octlpsolve 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. Under Windows, the dll should be in a directory specified by the PATH environment variables and under Unix/Linux in directory /lib, /usr/lib or a directory defined by LD_LIBRARY_PATH.

### Solve an lp model from Octave via octlpsolve

In the following text, octave:> before the Octave commands is the Octave prompt. Only the text after octave:> must be entered. Note that the default prompt also contains an incrementing number starting from one each time Octave starts. For this documentation, the default Octave was changed with the following command: PS1 = "\\s:> "

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

    octave:> [ret1, ret2, ...] = octlpsolve('functionname', arg1, arg2, ...)

The return values are optional and depend on the function called. functionname must always be enclosed between single or 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 Octave specific functions. Most of the lpsolve API routines use or return an lprec structure. To make things more robust in Octave, 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 Octave 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 Octave, nothing must be dimensioned in advance. The octlpsolve driver takes care of dimensioning all return variables and they are always returned as return value of the call to octlpsolve. Never as argument to the routine. This can be a single value as for get_objective (although Octave 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.

Note that you can get an overview of the available functionnames and their arguments by entering the following in Octave:

    >> help octlpsolve.m

### 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.m. You can see its contents by entering type example1.m)

    octave:> lp=octlpsolve('make_lp', 0, 4);
    octave:> octlpsolve('set_verbose', lp, 3);
    octave:> octlpsolve('set_obj_fn', lp, [1, 3, 6.24, 0.1]);
    octave:> octlpsolve('add_constraint', lp, [0, 78.26, 0, 2.9], 2, 92.3);
    octave:> octlpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], 1, 14.8);
    octave:> octlpsolve('add_constraint', lp, [12.68, 0, 0.08, 0.9], 2, 4);
    octave:> octlpsolve('set_lowbo', lp, 1, 28.6);
    octave:> octlpsolve('set_lowbo', lp, 4, 18);
    octave:> octlpsolve('set_upbo', lp, 4, 48.98);
    octave:> octlpsolve('set_col_name', lp, 1, 'COLONE');
    octave:> octlpsolve('set_col_name', lp, 2, 'COLTWO');
    octave:> octlpsolve('set_col_name', lp, 3, 'COLTHREE');
    octave:> octlpsolve('set_col_name', lp, 4, 'COLFOUR');
    octave:> octlpsolve('set_row_name', lp, 1, 'THISROW');
    octave:> octlpsolve('set_row_name', lp, 2, 'THATROW');
    octave:> octlpsolve('set_row_name', lp, 3, 'LASTROW');
    octave:> octlpsolve('write_lp', lp, 'a.lp');
    octave:> octlpsolve('get_mat', lp, 1, 2)
    ans = 78.260
    octave:> octlpsolve('solve', lp)
    ans = 0
    octave:> octlpsolve('get_objective', lp)
    ans = 31.783
    octave:> octlpsolve('get_variables', lp)
    ans =

      28.60000
       0.00000
       0.00000
      31.82759

    octave:> octlpsolve('get_constraints', lp)
    ans =

       92.3000
        6.8640
      391.2928

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. For example:

    octave:> obj=octlpsolve('get_objective', lp)
    obj = 31.783

Or without echoing on screen:

    octave:> obj=octlpsolve('get_objective', lp);

The last command 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:

    octave:> x=octlpsolve('get_variables', lp);
    octave:> b=octlpsolve('get_constraints', lp);

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

    octave:> x
    x =

      28.60000
       0.00000
       0.00000
      31.82759

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

    octave:> octlpsolve('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:

    octave:> lp=octlpsolve('make_lp', 0, 4);
    octave:> octlpsolve('set_lp_name', lp, 'mymodel');
    octave:> octlpsolve('set_verbose', 'mymodel', 3);
    octave:> octlpsolve('set_obj_fn', 'mymodel', [1, 3, 6.24, 0.1]);
    octave:> octlpsolve('add_constraint', 'mymodel', [0, 78.26, 0, 2.9], 2, 92.3);
    octave:> octlpsolve('add_constraint', 'mymodel', [0.24, 0, 11.31, 0], 1, 14.8);
    octave:> octlpsolve('add_constraint', 'mymodel', [12.68, 0, 0.08, 0.9], 2, 4);
    octave:> octlpsolve('set_lowbo', 'mymodel', 1, 28.6);
    octave:> octlpsolve('set_lowbo', 'mymodel', 4, 18);
    octave:> octlpsolve('set_upbo', 'mymodel', 4, 48.98);
    octave:> octlpsolve('set_col_name', 'mymodel', 1, 'COLONE');
    octave:> octlpsolve('set_col_name', 'mymodel', 2, 'COLTWO');
    octave:> octlpsolve('set_col_name', 'mymodel', 3, 'COLTHREE');
    octave:> octlpsolve('set_col_name', 'mymodel', 4, 'COLFOUR');
    octave:> octlpsolve('set_row_name', 'mymodel', 1, 'THISROW');
    octave:> octlpsolve('set_row_name', 'mymodel', 2, 'THATROW');
    octave:> octlpsolve('set_row_name', 'mymodel', 3, 'LASTROW');
    octave:> octlpsolve('write_lp', 'mymodel', 'a.lp');
    octave:> octlpsolve('get_mat', 'mymodel', 1, 2)
    ans = 78.260
    octave:> octlpsolve('solve', 'mymodel')
    ans = 0
    octave:> octlpsolve('get_objective', 'mymodel')
    ans = 31.783
    octave:> octlpsolve('get_variables', 'mymodel')
    ans =

      28.60000
       0.00000
       0.00000
      31.82759

    octave:> octlpsolve('get_constraints', 'mymodel')
    ans =

       92.3000
        6.8640
      391.2928

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 Octave routine to get the handle from the model name: get_handle.
For example:

    >> octlpsolve('get_handle', 'mymodel')
    0

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

    octave:> octlpsolve('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 Octave, all numerical data is stored in matrices; even a scalar variable. Octave also supports complex numbers (a + b * i with i=sqrt(-1)). octlpsolve can only work with real numbers. For example:

    octave:> octlpsolve('add_constraint', lp, [0.24, 0, 11.31, 0], 1, 14.8);

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

    octave:> octlpsolve('add_constraint', lp, a1, 1, 14.8);

Where a1 is a matrix variable.

Most of the time, octlpsolve 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:

    octave:> octlpsolve('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 Octave 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 Octave matrix.

### Sets

All numerical data is stored in matrices. Alphanumerical data, however, is more difficult to store in matrices. Matrices require that each element has the same size (length) and that is difficult and unpractical for alphanumerical data. In a limited number of lpsolve routines, alphanumerical data is required or returned and in some also multiple elements. An example is set_col_name. For this, Octave sets are used. To specify a set of alphanumerical elements, the following notation is used: { 'element1', 'element2', ... }. Note the { and } symbols instead of [ and ] that are used with matrices.

### Maximum usage of matrices/sets with octlpsolve

Because Octave 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 octlpsolve Octave 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 octlpsolve Octave driver however also allows specifying a vector to set the integer status of all variables at once. The API call is: return = octlpsolve('set_int', lp, column, must_be_int). The matrix version of this call is: return = octlpsolve('set_int', lp, [must_be_int]). The API call to return the integer status of a variable is: return = octlpsolve('is_int', lp, column). The matrix version of this call is: [is_int] = octlpsolve('is_int', lp)
Also note the get_mat and set_mat routines. In Octave 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.m. You can see its contents by entering type example2.m)

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

       0.00000  78.26000   0.00000   2.90000
       0.24000   0.00000  11.31000   0.00000
      12.68000   0.00000   0.08000   0.90000

    octave:> octlpsolve('solve', lp)
    ans = 0
    octave:> octlpsolve('get_objective', lp)
    ans = 31.783
    octave:> octlpsolve('get_variables', lp)
    ans =

      28.60000
       0.00000
       0.00000
      31.82759

    octave:> octlpsolve('get_constraints', lp)
    ans =

       92.3000
        6.8640
      391.2928

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:

    octave:> A=octlpsolve('get_mat', lp);
    octave:> X=octlpsolve('get_variables', lp);
    octave:> B = A * X
    B =

       92.3000
        6.8640
      391.2928

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:

    octave:> octlpsolve('get_constraints', lp)
    ans =

       92.3000
        6.8640
      391.2928

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

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

    octave:> C=octlpsolve('get_obj_fn', lp);
    octave:> X=octlpsolve('get_variables', lp);
    octave:> obj = C * X
    obj = 31.783

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:

    octave:> octlpsolve('get_objective', lp)
    ans = 31.783

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

### Script files

Octave can execute a sequence of statements stored in diskfiles. Script files mostly have the file type of ".m" as the last part of their filename (extension). Much of your work with Octave will be in creating and refining script files. Script files are usually created using your local editor.

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

The octlpsolve Octave distribution contains some example script files to demonstrate this.

To see the contents of such a file, enter the command 'type filename'. You can also edit these files with your favourite text editor (or notepad).

#### example1.m

Contains the commands as shown in the first example of this article.

#### example2.m

Contains the commands as shown in the second example of this article.

#### example3.m

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

#### example4.m

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

#### example5.m

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

#### example6.m

#### lp_solve.m

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 or type help lp_solve or just lp_solve 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:

    octave:> [obj, x]=lp_solve([-1, 2], [2, 1; -4, 4], [5, 5], [-1, -1], [], [], [1, 2])
    obj = 3
    x =

      1
      2

#### lp_maker.m

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 or type help lp_maker or just lp_maker to see its usage:

    octave:> help 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
                x >= vlb >= 0
                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:

    octave:> lp=lp_maker([-1, 2], [2, 1; -4, 4], [5, 5], [-1, -1], [], [], [1, 2])
    lp = 0

To solve the model and get the solution:

    octave:> octlpsolve('solve', lp)
    ans = 0

    octave:> octlpsolve('get_objective', lp)
    ans = 3

    octave:> octlpsolve('get_variables', lp)
    ans =

      1
      2

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

    octave:> octlpsolve('delete_lp', lp);

#### lpdemo.m

Contains several examples to build and solve lp models.

#### ex.m

Contains several examples to build and solve lp models. Also solves the lp_examples from the lp_solve distribution.

### 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.

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

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

    octave:> X = 0.1:0.05:40;
    octave:> Y1 = (15000. - 120*X)/210;
    octave:> Y2 = max((4000 - 110.*X)./30, 0);
    octave:> Y3 = max(75 - X, 0);
    octave:> Ytop = min([Y1; Y2; Y3]);
    octave:> bar(X, Ytop);

The red 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 the objective function P.

    octave:> hold on
    octave:> X=15:25:40;
    octave:> title('Solution space and objective')
    octave:> plot(X,(6315.63-143.0*X)/60.0);
    octave:> hold off

The line gives a picture of the objective function. All solutions that intersect with the red area are valid solutions, meaning that this result also fulfils the set constraints. The more the line goes to the right, the higher the objective value is. The optimal solution or best objective is a line that is still in the red 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:

    octave:> x = [1 1; 110 30] \ [75; 4000]
    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:

    octave:> P = [143 60] * x
    P = 6315.6

That is, $6315.6.

Note that these command are in script example3.m

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
                x >= vlb >= 0
                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:

    octave:> f = [143 60];
    octave:> A = [120 210; 110 30; 1 1];
    octave:> b = [15000; 4000; 75];
    octave:> lp = lp_maker(f, A, b, [-1; -1; -1], [], [], [], 1, 0);
    octave:> solvestat = octlpsolve('solve', lp)
    solvestat = 0
    octave:> obj = octlpsolve('get_objective', lp)
    obj = 6315.6
    octave:> x = octlpsolve('get_variables', lp)
    x =

      21.875
      53.125

    octave:> octlpsolve('delete_lp', lp);

Note that these command are in script example4.m

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:

    octave:> f = [143 60 195];
    octave:> A = [120 210 150.75; 110 30 125; 1 1 1];
    octave:> b = [15000; 4000; 75];
    octave:> lp = lp_maker(f, A, b, [-1; -1; -1], [], [], [], 1, 0);
    octave:> solvestat = octlpsolve('solve', lp)
    solvestat = 0
    octave:> obj = octlpsolve('get_objective', lp)
    obj = 6986.8
    octave:> x = octlpsolve('get_variables', lp)
    x =

       0.00000
      56.57895
      18.42105

    octave:> octlpsolve('delete_lp', lp);

Note that these command are in script example5.m

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 Octave 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 Octave 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?

    octave:> f = [110*1.3 30*2.0 125*1.56 75*1.8 95*.95 100*2.25 50*1.35];
    octave:> 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];

    octave:> b = [55000;40000;400;0;0;0];
    octave:> 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);
    octave:> solvestat = octlpsolve('solve', lp)
    solvestat = 0
    octave:> obj = octlpsolve('get_objective', lp)
    obj =  7.5398e+04
    octave:> x = octlpsolve('get_variables', lp)
    x =

       10.000
       10.000
       40.000
       45.652
       20.000
      250.000
       20.000

    octave:> octlpsolve('delete_lp', lp);

Note that these command are in script example6.m

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 Octave:

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 Octave 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 Octave:

    octave:> f = [4 2 1];
    octave:> A = [2 1 0; 1 0 2; 1 1 1];
    octave:> b = [1; 2; 1];
    octave:> l = [ 0 0 0];
    octave:> u = [ 1 1 2];

Now solve the linear program using Octave: Type the commands

    octave:> lp = lp_maker(f, A, b, [-1; -1; -1], l, u, [], 1, 0);
    octave:> solvestat = octlpsolve('solve', lp)
    solvestat = 0
    octave:> obj = octlpsolve('get_objective', lp)
    obj = 2.5000
    octave:> x = octlpsolve('get_variables', lp)
    x =

      0.50000
      0.00000
      0.50000

    octave:> octlpsolve('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 Octave command:

    octave:> 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:

    octave:> l = [-Inf -Inf -Inf];

Solve this and you get a different result:

    octave:> lp = lp_maker(f, A, b, [-1; -1; -1], l, u, [], 1, 0);
    octave:> solvestat = octlpsolve('solve', lp)
    solvestat = 0
    octave:> obj = octlpsolve('get_objective', lp)
    obj = 2.6667
    octave:> x = octlpsolve('get_variables', lp)
    x =

       0.66667
      -0.33333
       0.66667

    octave:> octlpsolve('delete_lp', lp)

### Overview of API routines

Note again that the Octave command 'help octlpsolve.m' gives an overview of all functions that can be called via octlpsolve with their arguments and return values.

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

### Extra Octave 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] = octlpsolve('get_col_names', lp)
  - The same as get_col_name. Implemented for backwards compatibility.
- [constr_type] = octlpsolve('get_constr_types', lp)
  - The same as get_constr_type. Implemented for backwards compatibility.
- [int] = octlpsolve('get_int', lp)
  - The same as is_int. Implemented for backwards compatibility.
- return = octlpsolve('get_no_cols', lp)
  - The same as get_Ncolumns. Implemented for backwards compatibility.
- return = octlpsolve('get_no_rows', lp)
  - The same as get_Nrows. Implemented for backwards compatibility.
- name = octlpsolve('get_objective_name', lp)
  - The same as get_row_name with row=0. Implemented for backwards compatibility.
- [row_vec, return] = octlpsolve('get_obj_fn', lp)
  [row_vec, return] = octlpsolve('get_obj_fun', lp)
  - The same as get_row with row 0. Implemented for backwards compatibility.
- name = octlpsolve('get_problem_name', lp)
  - The same as get_lp_name. Implemented for backwards compatibility.
- [costs] = octlpsolve('get_reduced_costs', lp)
  - The same as get_dual_solution. Implemented for backwards compatibility.
- [names] = octlpsolve('get_row_names', lp)
  - The same as get_row_name. Implemented for backwards compatibility.
- [obj, x, duals, return] = octlpsolve('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 = octlpsolve('mat_elm', lp)
  - The same as get_mat. Implemented for backwards compatibility.
- [handle_vec] = octlpsolve('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 = octlpsolve('read_lp_file', filename {, verbose {, lp_name}})
  - The same as read_LP. Implemented for backwards compatibility.
- lp_handle = octlpsolve('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 octlpsolve driver

#### Windows

To compile the Octave driver under Windows, the cygwin environment is needed. The following document describes what is needed for this: README.Windows. It may not be needed to build the Octave sources to compile the binary file, but the proposed cygwin and octave packages are needed to build a .oct file.
The build must be done from the cygwin prompt from the directory where the lpsolve octave files are located.
To make the compilation process easier, a script file can be used: ccc.win32
To make for release, just enter ./ccc.win32 and everything is build.

#### Unix/Linux

The build must be done from a shell prompt from the directory where the lpsolve octave files are located.
To make the compilation process easier, a script file can be used: ccc
To make for release, just enter sh ccc and everything is build.

#### All platforms

This compiles three source files: lpsolve.cpp, octave.cpp and hash.cpp
Then these are linked together to generate the octlpsolve.oct file.
The optional arguments to ccc are used for development. Source files can be provided and then only these are compiled. For example hash.cpp should only be compiled once while developing. So specifying lpsolve.cpp 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 octlpsolve. Should only be used for debugging purposes.

See also Using lpsolve from O-Matrix, Using lpsolve from MATLAB, Using lpsolve from Scilab, Using lpsolve from Python, Using lpsolve from PHP, Using lpsolve from R