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  • How to find minimum of nonlinear, multivariate function using Newton's method (code not linear algeb

    - by Norman Ramsey
    I'm trying to do some parameter estimation and want to choose parameter estimates that minimize the square error in a predicted equation over about 30 variables. If the equation were linear, I would just compute the 30 partial derivatives, set them all to zero, and use a linear-equation solver. But unfortunately the equation is nonlinear and so are its derivatives. If the equation were over a single variable, I would just use Newton's method (also known as Newton-Raphson). The Web is rich in examples and code to implement Newton's method for functions of a single variable. Given that I have about 30 variables, how can I program a numeric solution to this problem using Newton's method? I have the equation in closed form and can compute the first and second derivatives, but I don't know quite how to proceed from there. I have found a large number of treatments on the web, but they quickly get into heavy matrix notation. I've found something moderately helpful on Wikipedia, but I'm having trouble translating it into code. Where I'm worried about breaking down is in the matrix algebra and matrix inversions. I can invert a matrix with a linear-equation solver but I'm worried about getting the right rows and columns, avoiding transposition errors, and so on. To be quite concrete: I want to work with tables mapping variables to their values. I can write a function of such a table that returns the square error given such a table as argument. I can also create functions that return a partial derivative with respect to any given variable. I have a reasonable starting estimate for the values in the table, so I'm not worried about convergence. I'm not sure how to write the loop that uses an estimate (table of value for each variable), the function, and a table of partial-derivative functions to produce a new estimate. That last is what I'd like help with. Any direct help or pointers to good sources will be warmly appreciated. Edit: Since I have the first and second derivatives in closed form, I would like to take advantage of them and avoid more slowly converging methods like simplex searches.

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  • BSOD error 0x0000006B PROCESS1_INITIALIZATION_FAILED on boot

    - by DontCare4Free
    I reinstalled League of Legends because the patcher always gave me an error. However, out of complete stupidness I didn't uninstall the old installation first because I thought that it would simply replace the files. However, when the installer bar got to 100% it simply minimized. Then I closed the application from the task manager. I tried uninstalling it after a failed attempt to start it up. The same behavior as when I installed it. Then I tried reinstalling where it simply presented the InstallShield Modify/Repair/Remove menu and I selected repair. Nothing happened. Then I tried selecting Modify, then seeing that the only option (called DefaultFeature) was unchecked. Same behaviour as install/uninstall. After seeing that it still failed, I uninstalled again. And after that I deleted C:\Program Files (x86)\League of Legends manually. When I tried installing LoL again it still thought I had it, so I chose repair. This time something actually happened, but it installed the whole game to C:\Windows. Seeing what was going on I clicked cancel and then started it up to try uninstalling it. However, I got an error message about something not being registered and then the minimization to I decided to let it repair completely. Then I uninstalled it and it gave only the minimization. However, when I rebooted another application started up complaining about some library being absent. So I decided to do a system restore. After letting it complete I got a BSOD every time I tried starting up Windows normally or in safe mode. However, system recovery mode works, although the system recovery automatic repair does not fix it. After a bit of searching I found a Microsoft KB article about it (981833) and tried following the workaround instructions. Nothing happened. I am using Windows 7 Home Premium 64-bit and Ubuntu 10.04 LTS 64-bit installed with WUBI.

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  • SSMS Tools Pack 1.9.3 is out!

    - by Mladen Prajdic
    This release adds a great new feature and fixes a few bugs. The new feature called Window Content History saves the whole text in all all opened SQL windows every N minutes with the default being 30 minutes. This feature fixes the shortcoming of the Query Execution History which is saved only when the query is run. If you're working on a large script and never execute it, the existing Query Execution History wouldn't save it. By contrast the Window Content History saves everything in a .sql file so you can even open it in your SSMS. The Query Execution History and Window Content History files are correlated by the same directory and file name so when you search through the Query Execution History you get to see the whole saved Window Content History for that query. Because Window Content History saves data in simple searchable .sql files there isn't a special search editor built in. It is turned ON by default but despite the built in optimizations for space minimization, be careful to not let it fill your disk. You can see how it looks in the pictures in the feature list. The fixed bugs are: SSMS 2008 R2 slowness reported by few people. An object explorer context menu bug where it showed multiple SSMS Tools entries and showed wrong entries for a node. A datagrid bug in SQL snippets. Ability to read illegal XML characters from log files. Fixed the upper limit bug of a saved history text to 5 MB. A bug when searching through result sets prevents search. A bug with Text formatting erroring out for certain scripts. A bug with finding servers where it would return null even though servers existed. Run custom scripts objects had a bug where |SchemaName| didn't display the correct table schema for columns. This is fixed. Also |NodeName| and |ObjectName| values now show the same thing.   You can download the new version 1.9.3 here. Enjoy it!

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  • How do I set a default page in Pylons?

    - by Evgeny
    I've created a new Pylons application and added a controller ("main.py") with a template ("index.mako"). Now the URL http://myserver/main/index works. How do I make this the default page, ie. the one returned when I browse to http://myserver/ ? I've already added a default route in routing.py: def make_map(): """Create, configure and return the routes Mapper""" map = Mapper(directory=config['pylons.paths']['controllers'], always_scan=config['debug']) map.minimization = False # The ErrorController route (handles 404/500 error pages); it should # likely stay at the top, ensuring it can always be resolved map.connect('/error/{action}', controller='error') map.connect('/error/{action}/{id}', controller='error') # CUSTOM ROUTES HERE map.connect('', controller='main', action='index') map.connect('/{controller}/{action}') map.connect('/{controller}/{action}/{id}') return map I've also deleted the contents of the public directory (except for favicon.ico), following the answer to http://stackoverflow.com/questions/1279403/default-route-doesnt-work Now I just get error 404. What else do I need to do to get such a basic thing to work?

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  • What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

    - by Ein Doofus
    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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  • What is the best way to determine the path to the ISV directory?

    - by Luke Baulch
    MSCRM 4.0 Problem: I'm currently storing xml files in the ISV directory along with my web applications. From a plugin (or potentially a seperate app), I need to find an easy way to navigate to the ISV directory to read these xml files. This routine will be called extremely often, so processing minimization should be a strong consideration. Potential solutions: Registry: There is a registry key called 'WebSitePath' with the data 'C:\Inetpub\wwwroot\CRM'. Could potentially use this to build the path. (Will this be the same on all systems/installations?) IIS directory data: Looping through the DirectoryEntries of path '"IIS://localhost/W3SVC"' I could obtain the the web application where description is equal to "Microsoft Dynamics CRM". (Will this be the same on all systems/installations?) Webservice: Create one to read and return the data contained in these xml files The webservice would have easy access to its executing directory. Database: Store the data of these files in the database. Help: Can anyone suggest a simpler solution to obtaining and reading a file from the ISV directory? If not, which of the above solutions would be the quickest to process? Thanks for any and all contributions.

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  • Minimum-Waste Print Job Grouping Algorithm?

    - by Matt Mc
    I work at a publishing house and I am setting up one of our presses for "ganging", in other words, printing multiple jobs simultaneously. Given that different print jobs can have different quantities, and anywhere from 1 to 20 jobs might need to be considered at a time, the problem would be to determine which jobs to group together to minimize waste (waste coming from over-printing on smaller-quantity jobs in a given set, that is). Given the following stable data: All jobs are equal in terms of spatial size--placement on paper doesn't come into consideration. There are three "lanes", meaning that three jobs can be printed simultaneously. Ideally, each lane has one job. Part of the problem is minimizing how many lanes each job is run on. If necessary, one job could be run on two lanes, with a second job on the third lane. The "grouping" waste from a given set of jobs (let's say the quantities of them are x, y and z) would be the highest number minus the two lower numbers. So if x is the higher number, the grouping waste would be (x - y) + (x - z). Otherwise stated, waste is produced by printing job Y and Z (in excess of their quantities) up to the quantity of X. The grouping waste would be a qualifier for the given set, meaning it could not exceed a certain quantity or the job would simply be printed alone. So the question is stated: how to determine which sets of jobs are grouped together, out of any given number of jobs, based on the qualifiers of 1) Three similar quantities OR 2) Two quantities where one is approximately double the other, AND with the aim of minimal total grouping waste across the various sets. (Edit) Quantity Information: Typical job quantities can be from 150 to 350 on foreign languages, or 500 to 1000 on English print runs. This data can be used to set up some scenarios for an algorithm. For example, let's say you had 5 jobs: 1000, 500, 500, 450, 250 By looking at it, I can see a couple of answers. Obviously (1000/500/500) is not efficient as you'll have a grouping waste of 1000. (500/500/450) is better as you'll have a waste of 50, but then you run (1000) and (250) alone. But you could also run (1000/500) with 1000 on two lanes, (500/250) with 500 on two lanes and then (450) alone. In terms of trade-offs for lane minimization vs. wastage, we could say that any grouping waste over 200 is excessive. (End Edit) ...Needless to say, quite a problem. (For me.) I am a moderately skilled programmer but I do not have much familiarity with algorithms and I am not fully studied in the mathematics of the area. I'm I/P writing a sort of brute-force program that simply tries all options, neglecting any option tree that seems to have excessive grouping waste. However, I can't help but hope there's an easier and more efficient method. I've looked at various websites trying to find out more about algorithms in general and have been slogging my way through the symbology, but it's slow going. Unfortunately, Wikipedia's articles on the subject are very cross-dependent and it's difficult to find an "in". The only thing I've been able to really find would seem to be a definition of the rough type of algorithm I need: "Exclusive Distance Clustering", one-dimensionally speaking. I did look at what seems to be the popularly referred-to algorithm on this site, the Bin Packing one, but I was unable to see exactly how it would work with my problem. Any help is appreciated. :)

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  • Why Are Minimized Programs Often Slow to Open Again?

    - by Jason Fitzpatrick
    It seems particularly counterintuitive: you minimize an application because you plan on returning to it later and wish to skip shutting the application down and restarting it later, but sometimes maximizing it takes even longer than launching it fresh. What gives? Today’s Question & Answer session comes to us courtesy of SuperUser—a subdivision of Stack Exchange, a community-driven grouping of Q&A web sites. The Question SuperUser reader Bart wants to know why he’s not saving any time with application minimization: I’m working in Photoshop CS6 and multiple browsers a lot. I’m not using them all at once, so sometimes some applications are minimized to taskbar for hours or days. The problem is, when I try to maximize them from the taskbar – it sometimes takes longer than starting them! Especially Photoshop feels really weird for many seconds after finally showing up, it’s slow, unresponsive and even sometimes totally freezes for minute or two. It’s not a hardware problem as it’s been like that since always on all on my PCs. Would I also notice it after upgrading my HDD to SDD and adding RAM (my main PC holds 4 GB currently)? Could guys with powerful pcs / macs tell me – does it also happen to you? I guess OSes somehow “focus” on active software and move all the resources away from the ones that run, but are not used. Is it possible to somehow set RAM / CPU / HDD priorities or something, for let’s say, Photoshop, so it won’t slow down after long period of inactivity? So what is the deal? Why does he find himself waiting to maximize a minimized app? The Answer SuperUser contributor Allquixotic explains why: Summary The immediate problem is that the programs that you have minimized are being paged out to the “page file” on your hard disk. This symptom can be improved by installing a Solid State Disk (SSD), adding more RAM to your system, reducing the number of programs you have open, or upgrading to a newer system architecture (for instance, Ivy Bridge or Haswell). Out of these options, adding more RAM is generally the most effective solution. Explanation The default behavior of Windows is to give active applications priority over inactive applications for having a spot in RAM. When there’s significant memory pressure (meaning the system doesn’t have a lot of free RAM if it were to let every program have all the RAM it wants), it starts putting minimized programs into the page file, which means it writes out their contents from RAM to disk, and then makes that area of RAM free. That free RAM helps programs you’re actively using — say, your web browser — run faster, because if they need to claim a new segment of RAM (like when you open a new tab), they can do so. This “free” RAM is also used as page cache, which means that when active programs attempt to read data on your hard disk, that data might be cached in RAM, which prevents your hard disk from being accessed to get that data. By using the majority of your RAM for page cache, and swapping out unused programs to disk, Windows is trying to improve responsiveness of the program(s) you are actively using, by making RAM available to them, and caching the files they access in RAM instead of the hard disk. The downside of this behavior is that minimized programs can take a while to have their contents copied from the page file, on disk, back into RAM. The time increases the larger the program’s footprint in memory. This is why you experience that delay when maximizing Photoshop. RAM is many times faster than a hard disk (depending on the specific hardware, it can be up to several orders of magnitude). An SSD is considerably faster than a hard disk, but it is still slower than RAM by orders of magnitude. Having your page file on an SSD will help, but it will also wear out the SSD more quickly than usual if your page file is heavily utilized due to RAM pressure. Remedies Here is an explanation of the available remedies, and their general effectiveness: Installing more RAM: This is the recommended path. If your system does not support more RAM than you already have installed, you will need to upgrade more of your system: possibly your motherboard, CPU, chassis, power supply, etc. depending on how old it is. If it’s a laptop, chances are you’ll have to buy an entire new laptop that supports more installed RAM. When you install more RAM, you reduce memory pressure, which reduces use of the page file, which is a good thing all around. You also make available more RAM for page cache, which will make all programs that access the hard disk run faster. As of Q4 2013, my personal recommendation is that you have at least 8 GB of RAM for a desktop or laptop whose purpose is anything more complex than web browsing and email. That means photo editing, video editing/viewing, playing computer games, audio editing or recording, programming / development, etc. all should have at least 8 GB of RAM, if not more. Run fewer programs at a time: This will only work if the programs you are running do not use a lot of memory on their own. Unfortunately, Adobe Creative Suite products such as Photoshop CS6 are known for using an enormous amount of memory. This also limits your multitasking ability. It’s a temporary, free remedy, but it can be an inconvenience to close down your web browser or Word every time you start Photoshop, for instance. This also wouldn’t stop Photoshop from being swapped when minimizing it, so it really isn’t a very effective solution. It only helps in some specific situations. Install an SSD: If your page file is on an SSD, the SSD’s improved speed compared to a hard disk will result in generally improved performance when the page file has to be read from or written to. Be aware that SSDs are not designed to withstand a very frequent and constant random stream of writes; they can only be written over a limited number of times before they start to break down. Heavy use of a page file is not a particularly good workload for an SSD. You should install an SSD in combination with a large amount of RAM if you want maximum performance while preserving the longevity of the SSD. Use a newer system architecture: Depending on the age of your system, you may be using an out of date system architecture. The “system architecture” is generally defined as the “generation” (think generations like children, parents, grandparents, etc.) of the motherboard and CPU. Newer generations generally support faster I/O (input/output), better memory bandwidth, lower latency, and less contention over shared resources, instead providing dedicated links between components. For example, starting with the “Nehalem” generation (around 2009), the Front-Side Bus (FSB) was eliminated, which removed a common bottleneck, because almost all system components had to share the same FSB for transmitting data. This was replaced with a “point to point” architecture, meaning that each component gets its own dedicated “lane” to the CPU, which continues to be improved every few years with new generations. You will generally see a more significant improvement in overall system performance depending on the “gap” between your computer’s architecture and the latest one available. For example, a Pentium 4 architecture from 2004 is going to see a much more significant improvement upgrading to “Haswell” (the latest as of Q4 2013) than a “Sandy Bridge” architecture from ~2010. Links Related questions: How to reduce disk thrashing (paging)? Windows Swap (Page File): Enable or Disable? Also, just in case you’re considering it, you really shouldn’t disable the page file, as this will only make matters worse; see here. And, in case you needed extra convincing to leave the Windows Page File alone, see here and here. Have something to add to the explanation? Sound off in the the comments. Want to read more answers from other tech-savvy Stack Exchange users? Check out the full discussion thread here.     

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