Using Matlab C/C++ Math Library without Matlab or ITS Compiler
In this note, we will see how to make use of the Matlab C Math Library and C++ Math Library (see manuals and references below) provided by Matlab, and have it serve our TAO and PETSc optimization programs. We will link them together rather than simply using the filesystem for communication. Matrix inversion and matrixmatrix multiplication are taken as examples of the math library (other examples are eigenvalue, SVD, . We restrict ourselves to math library, though I think it will be easy to extend to other libraries such as MATLAB C/C++ Graphics Library. This note is NOT about how to convert an arbitrary Matlab .m file to C++, without using the expensive Matlab Compiler.
First, compare the price. As of 3 pm on August 6, 2007 (Sydney time GMT +10:00), a naked Matlab 7.4 without any toolbox costs USD 2,400 for individual license (maybe they will give you some not very useful toolboxes for free to promote). The Matlab Compiler 4.6, which converts Matlab .m code to C, costs USD 6,250.
This page also gives details about how to compile the code for my paper

Xinhua Zhang and Wee Sun Lee Hyperparameter Learning for Graph based Semisupervised Learning Algorithms Advances in Neural Information Processing Systems 19, 2009. [PDF] 
After compilation, run "./loo". Well, now you can only see that it complains about missing arg sig. When I have time, I will try to provide a more succinct example. Now just take it as an indication that our compilation and linking are both well done.
The versions of packages or tools used in this note are:
PETSc 2.3.0, TAO 1.8. We will not use MPI.
gcc version 3.3.5 (if on Debian 1:3.3.512) and gcc version 4.0.3 (if on Ubuntu 4.0.31ubuntu5)
See version considerations and license considerations in special notes.
The version of Matlab we will make use of is 6.5, which is installed on RSISE Debian machine, but not on Ubuntu machines (where only Matlab 7.2 is installed). Only the Matlab 6.5 on Debian has a Compiler installed, but the administrator reserved all the licenses so we can't use it.
But the approach below doesn't require the availability of Matlab on your own machine (as long as you can get some header files and libraries, see below). It works on both Debian and Ubuntu. So far, I haven't tested on WinXP. Refer to license considerations in special notes.
Steps
We will assume that all related files will be placed in the directory /home/usr/test. In the end, we will create three subfolders in /home/usr/test: include, bin, and toolbox. For more information about how to install PETSc and TAO on cygwin (or Linux machines), please read another note of mine.
1. Download the include.zip (179 KB, dead link now since I don't want to put myself in hot water) which contains necessary Matlab header files. Decompress it and put the folder "include" under /home/usr/test. If you have the Compiler toolbox installed, then the include.zip above is the folder /usr/local/matlab6.5/extern/include
2. Download the mglinstaller (free installer, 13 MB) provided by Matlab Compiler which installs the runtime library. Save it to /home/usr/test. Run "./mglinstaller" and it will install the Matlab runtime libraries under /home/usr/test/bin/glnx86. It will also generate a folder /home/usr/test/toolbox, which we will not use (at least not as explicitly as to my knowledge).
3. Download the ccpp_math_example.zip which contains the examples coming with Matlab. It has two folders, one for C and one for C++. Notice that they use different makefiles, because for C++ Math Library, we can only use g++ 2.95, no higher version! Decompress it and put the two folders in /home/usr/test.
4. In makefile, change MATLAB_ROOT to /home/usr/test, and run "make". It will create an executables.
General annotation of our approach
1. Source code. If you are interested to see how we called Matlab math library functions, pay attention to the function testAccuracyImport in loo.cpp. Basically, we called mlfInv, mlfAssign, mxGetPr, mxDestroyArray. We also used mlfEig and mlfSort (line 720, 721 in funciton dispEigs), mlfMpower (line 784 in funciton calPowerPtilde). Just mimic and refer to the references below.
2. makefile. Notice that we included some library files in LIBS. They are based on trial and error, i.e., basically how the linker complains. Some header/include and lib file directory information for TAO and PETSc was also manually given. Note that the Matlab library directory $MATLAB_LIB_DIR is pointed to the libraries installed by the mglinstaller in step 2. So is the include directory $MATLAB_INCL_DIR.
3. Libraries. It may be preferable to dynamically load Matlab C/C++ Math Library. So during linking, use rpathlink when you link. Then you need to add runtime library path: "export LD_LIBRARY_PATH=/home/usr/test/bin/glnx86:/usr/lib/:${LD_LIBRARY_PATH}".
Special notes
1. It is nothing new to call mlfXXX, mxXXX and mexXXX functions in the MEX files written in C++. But the MEX file requires that the final program be run in Matlab. In other words, it is used to call C/C++ programs from Matlab code. Now we completely eliminate the need of the expensive Matlab, both at compilation and at runtime.
2. Version considerations: The approach described in this note applies to Matlab 6.5 (maybe below as well). From Matlab 7 (R14), the C/C++ Math Library has been removed. In Matlab 7 and above, if you use the Compiler toolbox, an AES encrypted CTF file will be created after compiling .m code to C++ code. This CTF file is required at run time. So far, I am not able to hand craft this encrypted CTF file (or the decrypted version at run time).
On Matlab R12 (6.0) and below, there is a separate C/C++ Math Library, which can be chosen to install or not when the Matlab is installed. This library comes free with Matlab. The library version is 2.1 in R12. However in R13, this library was no longer provided separately, and it became a component of the expensive Compiler toolbox.
3. License considerations: If you don't have Matlab R12 or below, or you don't have the Compiler toolbox though you have Matlab R13, you may need to take some trouble to get the header files and mglinstaller (runtime libraries). So theoretically they are not free. But for compilation using gcc as in step 5, you do not need to acquire the Matlab license. So you have two choices:
i) Illegally ask your rich friend, who has Matlab (<R13) or Compiler for R13, to give you the header files (as I said above, /usr/local/matlab6.5/extern/include) and the mglinstaller (/usr/local/matlab6.5/extern/include);
ii) Buy ONE license only, so that you obtain the header files and library. Then all your team members can legally use the approach described here, because compilation doesn't require a license.
C/C++ Math Library Manuals and References
These documents can be used in Matlab R12 (6.0) or R13 (6.5):
* MATLAB C Math Library 2.1 User's Guide
* MATLAB C Math Library 2.1 Reference
* MATLAB C++ Math Library 2.1 User's Guide
* MATLAB C++ Math Library 2.1 Reference
Another tutorial that I found useful.