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Computing Graphics A joint newsletter of the Statistical Computing & Statistical Graphics Sections of the American Statistical Association. April 1993 Vol.4 No.1 COMPUTING GRAPHICS A WORD FROM OUR CHAIRS FEATURE ARTICLE Statistical Computing Saxpy, gaxpy, LAPACK, OneoftheperksoftheChairoftheStatisticalCom- puting Section is writing a column for this newsletter. and BLAS Imagine: I can write for several thousand members of Colin Goodall The Pennsylvania State University my profession, without the bene®t of refereeing. I get to tell you what I think, rather than what I know. Measuring Performance Maybe I'm a bit odd, but what I've been thinking about One of the best understood computational tasks is lin- is copyrighting and patenting of statistical software and ear algebra. Considerable effort has gone into fast and of computer material in general. My interest was piqued accurate code for these manipulations, e.g. LINPACK by an advertisement I received for a computer pack- (Dongarra et al. 1979), EISPACK, and most recently age that would display a high dimensional plot using a LAPACK (Anderson et al. 1992). The speed of these patented algorithm. The name of the method was jar- computations is measured in mega ¯ops (MFLOPS), or gon, so I could tell nothing from the advertisement about millions of ¯oating point instructions per second. Each the program and what it did. Mainly, what the adver- ¯oating point instruction is a single arithmetic opera- tisement did was make me wonder just what it meant for tion, e.g. a multiplication, a divide, an addition or sub- an algorithm to be patented. Was I supposed to believe traction, performed in full ¯oating point precision arith- that patenting was a substitute for peer review? Did it metic, usually 64 bits double precision. Two common imply certi®cation? Did it mean that I could not com- benchmarks for comparing performance are Dhrystone, pute this graph, whatever it is, with my own computer which measures speed of integer arithmetic computa- code unless I paid a royalty? tions, and Whetstone for ¯oating point computations. Assuming that most of us non-lawyers are as ignorant These measure not just the speed of the CPU but also of copyrighting and patenting as I was, I thought a compiler performance. Dhrystone performance, mea- short summary of what I've learned might be of in- sured in millions of instructions per second, can equal terest. Finding the information was easy: one call to and possibly exceed the clock speed of the CPU. my university's patent of®ce brought a few relevant pa- A more exacting benchmark involves a practical lin- pers, particularly [1], and a copy of the law. A review of ear algebra task, speci®cally the 100 100 LINPACK my university library's on-line card catalog gave nearly benchmark (Dongarra (1993)). This measures the speed 200 references, including a journal, Software Protec- achieved, in MFLOPS, in computing the Cholesky de- tion, which has been published since 1982. composition of an arbitrary 100 100 symmetric ma- Copyright and patent are very different. The basis trix, using a ®xed set of FORTRAN code. The numbers for copyright is contained in the U. S. Constitution, obtained from this benchmark are surprising: For exam- which gives to Congress the authority ª[t]o promote the ple a SparcStation II, with a processor rated at around Progress of Science and the useful Arts by securing for 25 MFLOPS, has a 100 100 LINPACK speed of 4.0 Limited Times to Authors and Inventors the exclusive MFLOPS (Dongarra (1993)). Put another way, the theo- n Right to their respective Writings and Discoveriesº [2]. retical requirement for an n Cholesky decomposition 3 2 = + n n = Exactly what can be covered by copyright was spelled is n 3 2 ¯ops, or 353,333 ¯ops when 100. CONTINUED ON PAGE ?? CONTINUED ON PAGE ?? EDITORIAL In preparing this issue we have realized yet again the herculian efforts of the newsletter's founding editors, ªThree in 93 and four in 94º was proclaimed as the Sallie Keller-McNulty and Dan Carr. We hope we can rallying call of the new editors of the joint Statistical live up to the standards they have set for us. Computing and Statistical Graphics newsletter. If we have succeeded then this ®rst issue of 1993 should be in James L. Rosenberger your hands before the April Interface meeting. We are Editor Statistical Computing Section planning to mail the second issue before the Joint Statis- [email protected] tical Meetings in August, and the third sometime around Mike Meyer Thanksgiving. More issues mean the newsletter can be Editor, Statistical Graphics Section more timely, provide announcements and encourage di- [email protected] alogue. Please use your newsletter to communicate with the membership of the two largest sections of the ASA. Our deadlines for the remaining issues in 1993 are the SECOND FEATURE last day of June and October. Many regular columns will continue, but we solicit your Production of help with new ideas and offers to write columns or once- Stereoscopic Displays only pieces. Please keep those e-cards and e-letters coming! for Data Analysis This issue has two feature articles. The ®rst feature de- Daniel B. Carr George Mason University scribes the availability and discusses the design of public domain matrix and linear algebra routines. Many aca- Dedicated to David L. Hall, colleague and friend. demic computer installations can make available high quality subroutines of the standard algorithms without Stereoscopic displays help the analyst escape from the the need to purchase or lease commercial software pack- limited domain of 2-D visualization into the natural do- ages, e.g. IMSL or NAG. Algorithms are available, as main of 3-D visualization. The goal of producing 3-D described by Colin Goodall, to anyone with FTP soft- scatterplots motivates much of the following discussion. ware and access to the internet. The goal has strong implications in terms of selecting a stereo projection. In the every day world, familiarity The second feature, about graphics and stereoscopic dis- with objects and many depth cues facilitates fusion of plays, is like the Sunday night mini-movie on network left and right retinal images into a stereo image. Monoc- television. It looks like a feature article, but is really the ular depth cues include linear perspective (objects of ®rst episode of a new column. Dan Carr has stepped equal size transect areas inversely proportional to their down as editor but couldn't resist the challenge of a distance), interposition or occlusion (when one object regular column. The graphic images which accompany is in front of another it obscures the more distant ob- this article should also be seen as the beginning of more ject), shadows (we generally assume light comes from innovative graphical material which we would like to above), detail perspective (no ®ne detail appears in dis- print. tant objects due to limited visual acuity), and aerial perspective (greater optical depth through the air leads The Newsletter is now being set/typeset in LATEX. Af- ter three years of colorful newsletters we have tried to to a blue shift). For most elementary 3-D scatterplots restrain ourselves to typographic spice and a change in prior knowledge about the form to be perceived is lim- format. Neither of us has any sense of color, so we ited and monocular cues are restricted, so care must be will take the conservative (and probably boring) tack taken in the selection of a stereo projection. and use black text on a neutral background. We want to Two In®nite Families of Reasonable Stereo credit Kevin Fox, the design artist from Penn State, for Projections the new masthead and for keeping our link to the past Different geometric models lead to different stereo pro- with the intersecting circles punctuating the articles. jections. (Geometric models are idealized in that each Submissions should be sent by email to either of the eye has a blind spot, a region of high resolution, and editors. If you can prepare your article in TEXorLATEX various imperfections.) A simple model (Newman and that will make our lives just a little easier. Otherwise Sproull 1979) presumes that the eyes converge on a sin- plain old ASCII format is ®ne. gle focal point and constructs left and right images by 2 Statistical Computing and Statistical Graphics Newsletter April 1993 projecting onto left and right projection planes. The 0). For the right eye this yields projection planes contain the focal point and are orthog- s [x; y ; z e= ; ;d] + e= ; ;d=x ;y ; r 2 0 2 0 r 0 onal to the respective lines of site. This ®xed-focal- 1 point model is appropriate for advanced dynamic sys- Solving both right-eye and left-eye equations for s based tems that update immediately as the eyes change their on the z coordinate and substituting yields: focal point. However, the ®xed-focal-point projection x = dx ez = =d z does not correspond to the data analyst's typical stereo- r 2 = dx + ez = =d z viewing scenario. Valyus (1962) states, ªit has been x l 2 (2) shown experimentally that eye movements performed = dy =d z when stereoscopic pictures are viewed are similar to y those performed in observing a real object. As the The fact the both left and right images have the same gaze is transferred from one object to another the eyes y coordinate is evident from geometric considerations. perform conjugate movements directed to the subjec- Consider a data point appearing behind the projection tively most important regions, and at the same time co- plane (or viewing screen).
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