Embedded Systems Design - August 2008 - (Page 15)

In this issue, I’ve conyou’re moving elements to The upside is, you can get larger elements centrated on the new ﬁle, the diagonal, you’re shufﬂing the matrix, much like a Rudown that critical diagonal, and therefore SimpleMat.cpp. Next bik’s cube. As you do so, you time, we’ll get back to the the highest accuracy possible. must record each shufﬂe, so C++ class called Matrix. that at the end of the process, I think you’ll ﬁnd that, you can put it back into orarmed with the functions operations. For my matrix class, I aim der. Because full pivoting uses both row in SimpleMat.cpp (available on to keep my focus on the general form of www.embedded.com/code), additions to and column transformations, the shufthe matrix and let the operations on ﬂe/ unshufﬂe process takes longer and that class will go smoothly. See you that class sufﬁce. uses a bit more memory. then. ■ The upside is, you can get larger elements down that critical diagonal, and therefore the highest accuracy possible. The IBM programmers thought this was worth the extra work, and I agree. Which is why I’ve been using the algorithm for lo these 40+ years. I should mention that Gauss-Jordan is not the only way to invert a matrix. More modern methods involve factoring the matrix into two parts. The LU decomposition, for example, involves facMicro Digital provides integrated USB toring the matrix into two triangular matrices. This process gives a little better solutions that run out of the box with our performance if you’re really seeking the SMX® RTOS, ﬁle system, and TCP/IP stack. matrix inverse, as you do to solve EquaThese robust, high-performance USB solution 7 via Equation 8. However, if you tions are written in ANSI-C, and can run on have to solve many such linear equaany hardware platform, with SMX, another tions, involving the same matrix A, LU RTOS, or stand-alone. Connect with us decomposition is much faster. today at www.smxrtos.com/usb. Several other decomposition algorithms exist. Each has its advantages. However, if you want the matrix inLook like to a PC: USB Controllers Supported: Connect to: OHCI, UHCI, EHCI, OTG verse explicitly, and your matrix is relAtmel AT91 • Cirrus EP USB disk drive USB disk drives atively small (say less than 20x20), ColdFire • Freescale i.MX USB serial device USB serial devices you’ll find mInv hard to beat. Luminary LM3S • Maxim 3421 Connect with the leader in embedded USB software. STILL TO COME With the functions in SimpleMat.cpp, we have most of the matrix operations we may ever need. Not all, however. The world of matrix algebra is particularly rich in mathematical operations. One that comes to mind is matrix diagonalization, which I’ll be adding later. There are other operations that we may never add. Many special classes of matrices exist, including diagonal, triangular, tridiagonal, and symmetric, to name a few. Each of these classes has its own set of specialized operations, and many numerical systems directed at matrix algebra include a host of such USB keybds, mice, HIDs USB audio devices USB modems USB printers USB-to-Ethernet adapters USB-to-serial adapters USB-to-WiFi w/WEP & WPA USB keyboard & mouse Audio with MIDI Ethernet over USB (RNDIS) Composite devices Multi-port serial NXP ISP, LPC • Sharp LH7 ST Micro STR7, 9, STM32 Features: USB 2.0 compliant • Low, full & high speed • All transfer modes Small & fast • Easily portable Standalone operation • Royaltyfree cap licensing • Full Source Code USB SOFTWARE LEADER 800.366.2491 sales@smxrtos.com Visit us at Booth #202 www.smxrtos.com/usb www.embedded.com | embedded systems design | AUGUST 2008 15 http://www.embedded.com/code http://www.smxrtos.com/usb http://i.MX http://www.smxrtos.com/usb http://www.smxrtos.com/usb http://www.embedded.com

Table of Contents Feed for the Digital Edition of Embedded Systems Design - August 2008

Embedded Systems Design - August 2008 Contents Number Include Parity Bit Programmer's Toolbox Cover Feature: Virtualization for Embedded X86 Multiprocessor Applications Wanted: Industry Standards for Benchmarking Embedded VMM Hypervisors Achieving Cache Coherence in a MIPS32 Multicore Design Memory Allocation in C Advertising Index Break Points Marketplace

Embedded Systems Design - August 2008

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