Technical Computing

Technical Computing Description Topics

• The Power of Technical Computing with MATLAB
• Data Analysis and Exploration
• Mathematical Algorithms to Build On
• Modeling and Simulation
• Visualization and Image Processing
• Programming and Application Development
• Distributed and Parallel Programming

Mathematical Algorithms to Build On

MATLAB provides a robust foundation for numerical computing, mathematical modeling, and customized algorithm development. These activities are supported by:

• A foundation of core mathematical algorithms
• Application-specific toolbox algorithms
• A flexible environment for algorithm development and deployment

A multidimensional surface created using a rational spline and its Taylor polynomial.

Rely on Trusted MATLAB Algorithms

MATLAB contains an extensive collection of core mathematical algorithms for numerical computing. These powerful numerical capabilities are built upon the LAPACK and optimized BLAS linear algebra libraries. By combining these highly optimized core computing routines with additional leading edge methods you can access the fastest and most robust numerical routines available.

The math is optimized for matrix operations, so you can use it instead of low level languages like C and C++, with equal performance, but less programming. MATLAB includes functions for:

• Trigonometric and other
• Polynomial functions fundamental math operations
• Ordinary differential equations
• Linear algebra
• Normal and sparse matrix operations
• Signal processing
• Nonlinear methods
• Geometric analysis

Here the Statistics Toolbox is used to model the chemical reaction rate of an experiment using the toolbox's design of experiments and surface fitting capabilities (left). Also shown is a beta distribution likelihood surface and confidence regions for estimated parameters (right). Click on image to see enlarged view.

Application-Specific Toolbox Algorithms

The MathWorks and third-party partners develop toolboxes that extend the capabilities and breadth of MATLAB in a variety of domains. MATLAB toolboxes are collections of highly optimized, application-specific algorithms written by world-class experts in their fields. By relying on their work, you can explore and apply innovative, leading-edge theory and techniques without writing code.

These toolboxes provide application-specific functions, GUIs, and custom plot types for tasks requiring signal and image processing, data analysis and modeling, mathematics, finance and control system design. For example, you can model data using the Statistics Toolbox, perform quadratic programming using the Optimization Toolbox, use the Signal Processing Toolbox to visualize spectral data, and work with neurocontrol applications within the Neural Network Toolbox. These toolboxes include thousands of application-specific toolbox functions in areas such as:

Curve Fitting Filter design Statistics Communications Optimization Wavelets Spline

Image processing Symbolic math Control system design Partial differential equations Neural networks Signal processing Fuzzy logic

For a complete list of toolboxes please visit our product pages.

The spectrogram demo from the Signal Processing Toolbox allows quick and intuitive access to a signal's spectrogram, time-slice, and frequency slice. This GUI is fully equipped with context-sensitive help and provides easy access to basic utilities for changing the colormap and focusing in on a portion of the signal. Click on image to see enlarged view.

Algorithm Development

Whether you are using existing algorithms or inventing your own, MATLAB provides an environment where you can experiment. With MATLAB you don't have to develop algorithms from scratch or work with complicated interfaces to external libraries, as you would frequently need to do with C and C++. You can write algorithms in MATLAB just as you would express them mathematically. In addition, toolbox functions are implemented in the open MATLAB language. This gives you access to the source code and algorithms and allows you to learn from and customize existing algorithms, or develop your own.

Here MATLAB and the Optimization and Financial Toolboxes are used in combination to create a GUI-driven program that optimizes a portfolio of mutual funds. The light blue line shows the "efficient investment frontier." The red mark shows the optimal investment point for a target return value. The fund allocation, expected return, and volatility for the optimal investment are also calculated and shown. Click on image to see enlarged view.