## Matrix Search Algorithm Using Binary Search Trees

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But it is also a tool that is of value to operations researchers for designing their own algorithms, for doing quick simulations, or for teaching operations research and statistics. As a programming language, you can use GAUSS to write compact programs given the number of matrix-based statistical and financial functions already built into the language.

Moreover, these programs can be compiled so that you do not actually have to run a program for several minutes only to find a typo in the last line. As an added plus, you can read and write data in the form of matrices into text files, into binary files and into Microsoft Excel spreadsheets. GAUSS is a computer language for numerical computation, its attraction being its handling of matrices in the same way as scalars.

Note that the blank spaces on both sides of "L" and "U" are required, creating problems for those used to more modern programming languages. These matrix operators not only make it easy for users to create even higher-level procedures and for vendors, including Aptech Systems, to provide many specialist functions.

For example, there is a large set of functions specifically designed for finance: These functions are not easy to program as one of us can attest so it is very handy to have these as functions.

There are also other finance- or econometrics-related programs written in GAUSS in the public domain, as will be detailed later. Then there is non-linear optimization that is catered for with Qnewton, quadratic programming that uses Qprog, and solution of a system of non-linear equations that full review what is the binary matrix programming eqSolve. These include full review what is the binary matrix programming to calculate the correlation matrix, meanc to calculate the mean value of each column of the given matrix, ols to perform ordinary least squares regression and pdfn to calculate standard normal probability density function values.

In the public domain, one can even find improved versions of some of these statistical procedures e. GAUSS also provides many functions for scientific computation.

These include differentiation and integration, linear algebra, eigenvalue, fourier transforms and random number generators rndnb generates a negative binomial pseudo random number, rndLCbeta calculate a beta pseudo random number. One library from Econotron Software allows linking to Maplesoft's Maple software that allows symbolic computation.

Operations research professionals can get add-in modules for linear programming, time series and maximum likelihood. Those working on the marketing interface may find a recently released application sold separately from the basic GAUSS software called Discrete Choice useful for handling discrete models like multinomial logit, conditional logit and nested logit.

Finally, GAUSS can be used to create graphs and pictures of various types, as well as manipulate these with a graphics editor. Moreover, in the reviewed version 5. Next we wrote a simple program as follows: Next, we skimmed through the User Guide with more attention to the chapter on the programming language constructs.

For the program we had in mind, we needed to create arrays for orders and for inventory levels over time at different supply chain nodesgo through iterative loops for different parameter settings and over timecreate random numbers for forecast error in each time period and calculate variance.

We also looked at the Language Reference Guide to figure out how to compute variance. We found that splitting help between the User Guide and a Language Reference to be quite confusing to beginners like us even though after some time it is clear that language constructs are to be found in the former and the functions in the latter. The "help" system is similarly split up, and our suggestion to Aptech would be to have an integrated system in the graphical user interface where everything could be found in one place, a good model being Wolfram's Mathematica software.

We then set about translating a program written in another software Mathematica to study the bullwhip effect. We had arrays declared with length to be determined at runtime.

In the GAUSS manuals, at first we did not find "dynamic allocation" of vector length, so we got past this problem by defining the array length at compile time, e. Later, however, we did find a reference for the call matalloc similar to that in C language in the Language Reference to dynamically allocate memory for a matrix. As a programming language, GAUSS has the feel of Fortran given its case-independence and procedures like gosub, but it also has the powerful set full review what is the binary matrix programming string manipulation functions taken straight out of the C language.

The language could be modernized by strengthening compile level errors requiring all variables to be declared, for instance and by better handling of whitespace spaces and newline. As already mentioned, the latter can cause errors that are puzzling for new users, e. Lines that are too long can cause strange compile-time errors but lines that are broken up by newline characters also cause problems. Given that GAUSS is primarily a programming language, its lack of a good programming environment is quite noticeable.

The program editor in the Windows versions has much more features than Notepad in terms of offering colors and highlighted keywords but does not help in anticipating the function calls you are trying to make. If you intend to use GAUSS frequently and you are already familiar with some other editor like Emacs or Epsilon, you may prefer to stick with that. Aptech needs to provide a better programming environment that helps users, for instance, by lining up your code automatically or in anticipating function calls you are trying to make and finding more about these.

A good model is the programming environment provided by Borland, eg. Using Help and the Manuals GAUSS was originally a terminal application that is still available along with a Windows-based one that **full review what is the binary matrix programming** still in early stages. The manuals also need to be expanded, integrated and made accessible centrally through the "help" feature.

Take for instance, the entry on transposing matrices: It would be good for a cross-reference to have been made to this in the entry for atranspose. As such, you may need to subscribe to Aptech's Premium Services to get support. Although there are a number of functions for both scalars and matrices level, there are few at the level of scalars alone, perhaps to avoid confusion. For example, we had to define min a,b as a procedure ourselves for scalars a and b. We reproduce a simplified version of the program we created for this review in Figure 2.

Regarding output, you can print to text files or to the screen and also to MS Excel spreadsheets. For printing to screen or to a text file, the default number of characters for a line is 80, but you can print your output in a wider file. It took us some time to hunt for information and finally found it in one of the Guide pdf files. The second and better alternative is to save your results to a matrix and then write that matrix directly into an Excel spreadsheet.

However, this means storing all results in memory specifically in a matrix form that may not be suitable for all types of results but you can do line-by-line output with some string manipulation within your code. Still, this option is better than writing to text files because accuracy of the numbers is preserved when you write to a spreadsheet directly.

Our experience was with the Windows version, specifically with Windows After some starting hiccups, full review what is the binary matrix programming were able to install and run the software. There are a number of files in the download directory including that with a Quick Guide in pdf format that should be downloaded first because this will tell you which files should be downloaded. Upon unzipping downloaded files, you can click on the "setup" file.

An install program takes you through the steps, the last of which generates full review what is the binary matrix programming about your computer. You must e-mail this information to license aptech. You can cut-and-paste the information that is e-mailed to you into a "gauss.

Our hiccup was that the machine in question was a laptop with a docking station that needs to be registered differently. Areas of Improvement We have already said that the help system the manuals, and the programming environment could use improvement, modernizing and updating.

In addition, concerns have been raised regarding numerical stability of some of the statistical and the equation-solving procedures in comparison to other statistical packages and regarding randomness of the random number generator [Vinod ]. There is a mailing list called Gaussians.

To subscribe or unsubscribe from this list, send the command subscribe gaussians in the body of an email message not on the subject line to majordomo eco. To access archives, **full review what is the binary matrix programming** www. The site also provides links to other resources on the Web. Aptech also provides numerous links at its own Web site http: Overall Summary GAUSS has been a workhorse for many financial, econometric and statistical professionals, researchers and students.

For operations researchers, it is a good tool for matrix manipulations and for teaching classes on matrix algebra or algorithms. So most users with rudimentary programming skills will find GAUSS easy to pick up and do useful things with in a few hours.

Its bare bones approach appears to translate into speedy results from concepts to results for an expert user, but the same approach is a limitation for new users more used to mouse-and-click than to the so-called full review what is the binary matrix programming applications.

It has recently been made available as a bit application on Sun's Solaris platform. Aptech also has an annually renewable premier service available via e-mail.

Visit their Web site to download the contract form. Specific user types may e-mail corpsw Aptech. For other countries, see the Aptech Web site, www. Pricing Information Aptech's products are competitively priced for the mathematical and statistical software market.

Potential customers are welcome to contact Aptech or local dealers for pricing configured for customers' specific systems and needs. Vendor Comments Editor's note: Following are comments from Ron Schoenberg, Ph. GAUSS is first of all a programming language. The tests he made were of source code he himself had written in GAUSS, and any failure of precision he found should be attributed to the design of his own algorithms rather than to any feature of GAUSS.

In fact he didn't do this at all. Thus he completely full review what is the binary matrix programming the criticism as about GAUSS' random number generator when it actually should have been directed at his own code. Moreover his own code is seriously flawed because it doesn't make any sense to write a linear congruential generator using floating point numbers. The remaining issues in his review suffer from the same fundamental flaw. GAUSS is a matrix programming language designed to make it easier for professionals who don't have the time or desire to learn C or Fortran for solving statistical or applied mathematical problems.

And this is accomplished by having a matrix type that needs no compile-time allocation but are sized "on-the-fly" at run-time, and which allows for natural intuitive expressions that look like the formulas in the text books. If the user's arguments are scalars, concatenate them full review what is the binary matrix programming a vector: After reading the review and the material at our Web site www.

GAUSS is accessible to a non-programmer professional, and it dramatically shrinks development time, all without significant loss of speed of execution and scalability of the problem.