The aim of this thesis is to create an educational material for creating graphical user interfaces in MATLAB. The reader will learn the basic procedures of the GUI creation, get to know the various graphic objects and learn about the GUIDE environment, which is intended for the actual application development. Text is supplemented by practical examples of source code fragments as much as possible. All material is accompanied by two functional sample applications with their source code.

MATLAB is an array language, initially popular for rapid prototyping, but is now being in-creasingly used to develop production code for numerical and scientific applications. Typical MATLAB programs have abundant data parallelism. These programs also have control flow dominated scalar regions that have an impact on the program’s execution time. Today’s com-puter systems have tremendous computing power in the form of traditional CPU cores and also throughput-oriented accelerators such as graphics processing units (GPUs). Thus, an approach that maps the control flow dominated regions of a MATLAB program to the CPU and the data parallel regions to the GPU can significantly improve program performance. In this work, we present the design and implementation of MEGHA, a compiler that auto-matically compiles MATLAB programs to enable synergistic execution on heterogeneous pro-cessors. Our solution is fully automated and does not require programmer input for identifying data parallel regions. Our compiler identifies data parallel regions of the program and com-poses them into kernels. The kernel composition step eliminates a number of intermediate arrays which are otherwise required and also reduces the size of the scheduling and mapping problem the compiler needs to solve subsequently. The problem of combining statements into kernels is formulated as a constrained graph clustering problem. Heuristics are presented to map identified kernels to either the CPU or GPU so that kernel execution on the CPU and the GPU happens synergistically, and the amount of data transfer needed is minimized. A heuristic technique to ensure that memory accesses on the CPU exploit locality and those on the GPU are coalesced is also presented. In order to ensure that data transfers required for dependences across basic blocks are performed, we propose a data flow analysis step and an edge-splitting strategy. Thus our compiler automatically handles kernel composition, mapping of kernels to CPU and GPU, scheduling and insertion of required data transfers. Additionally, we address the problem of identifying what variables can coexist in GPU memory simultaneously under the GPU memory constraints. We formulate this problem as that of identifying maximal cliques in an interference graph. We approximate the interference graph using an interval graph and develop an efficient algorithm to solve the problem. Furthermore, we present two program transformations that optimize memory accesses on the GPU using the software managed scratchpad memory available in GPUs. We have prototyped the proposed compiler using the Octave system. Our experiments using this implementation show a geometric mean speedup of 12X on the GeForce 8800 GTS and 29.2X on the Tesla S1070 over baseline MATLAB execution for data parallel benchmarks. Experiments also reveal that our method provides up to 10X speedup over hand written GPUmat versions of the benchmarks. Our method also provides a speedup of 5.3X on the GeForce 8800 GTS and 13.8X on the Tesla S1070 compared to compiled MATLAB code running on the CPU.

This dissertation presents the solution of difference equations and focuses on a method of difference equations solution with the aid of eigenvectors. The first part reminds the basic terms from area of difference equations such as dynamic of difference equations and linear difference equations of first order and higher order. Then the second section recalls also the system of difference equations including the fundamental matrix and general solution description. Afterthat, the method of solving the difference equations with a variation of constants and transform of scalar equations to the system are shown. The second part of the dissertation analyses some known algorithms and methods for the solution of linear difference equations. The Z-transform, its importance and usage for finding the solution of difference equation is recalled. Then the discrete analogue of Putzer's algorithm is mentioned because this algorithm was often used to check the results obtained by the newly described algorithm in further parts of this thesis. Also some ways of the system matrix power are stated. The next section then describes the principle of Weyr's method which is the basic point for further development of the theory including the presentation of the research results gained by Jiří Čermák in this area. The third part describes own solution of the difference equations system via eigenvectors based on the principle of Weyr's method for differential equations. The solution of system of linear homogeneous difference equtions with constant coefficients including the proof is presented and this solution is then extended to nonhomogeneous systems. Consequently to the theory, the influence of a nulity and the multiplicity of roots on the form of the solution is discussed. The last section of this part shows the implementation of the algorithm in Matlab program (for basic simpler cases) and its application to some cases of difference equations and systems with these equations. The final part of the thesis is more practical and it presents the usage of the designed algorithm and theory. Firstly, the algorithm is compared with Z-transform and the method of variation of constants and it is illustrated how to obtain the same results by using these three approaches. Then an example of current response solution in RLC circuit is demonstrated. The continuous case is solved and then the problem is transferred to discrete case and solved with the Z-transform and the method of eigenvectors. The obtained results are compared with the result of the continuous case.