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  • Need to organize words based on their components, any other way aside from brute force?

    - by Lathan
    I'm not sure if this process has a name. I have some words (about 9,000). They are in Japanese, but I'll try to explain this using English words. I want to categorize the words by the components (in English, letters). A B C act bar play This should create: A: play B: bar C: act Now, 'a' appears in all 3 words, but I want to make sure that each category (letter) has at least word. Now, it would make sense to delete a word after it's used, but there are a few cases where 2 letters make up one word and that's each letter's only word--so I'd like to account for that somehow. Is there an approach for solving this aside from brute force? Dynamic programming perhaps? Even a name for this process (if it exists) would be great.

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  • Adding Extra Hard Drives Debian Fdisk

    - by Belgin Fish
    well I just got a new server and it's a little different than what I'm use to, when I run cfdisk I get WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted. Disk /dev/sda: 3000.6 GB, 3000592982016 bytes 255 heads, 63 sectors/track, 364801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000 Device Boot Start End Blocks Id System /dev/sda1 1 267350 2147483647+ ee GPT Partition 1 does not start on physical sector boundary. WARNING: GPT (GUID Partition Table) detected on '/dev/sdb'! The util fdisk doesn't support GPT. Use GNU Parted. Disk /dev/sdb: 3000.6 GB, 3000592982016 bytes 255 heads, 63 sectors/track, 364801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000 Device Boot Start End Blocks Id System /dev/sdb1 1 267350 2147483647+ ee GPT Partition 1 does not start on physical sector boundary. WARNING: GPT (GUID Partition Table) detected on '/dev/sdc'! The util fdisk doesn't support GPT. Use GNU Parted. Disk /dev/sdc: 3000.6 GB, 3000592982016 bytes 255 heads, 63 sectors/track, 364801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000 Device Boot Start End Blocks Id System /dev/sdc1 1 267350 2147483647+ ee GPT Partition 1 does not start on physical sector boundary. WARNING: GPT (GUID Partition Table) detected on '/dev/sdd'! The util fdisk doesn't support GPT. Use GNU Parted. Disk /dev/sdd: 3000.6 GB, 3000592982016 bytes 255 heads, 63 sectors/track, 364801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000 Device Boot Start End Blocks Id System /dev/sdd1 1 267350 2147483647+ ee GPT Partition 1 does not start on physical sector boundary. WARNING: GPT (GUID Partition Table) detected on '/dev/sdf'! The util fdisk doesn't support GPT. Use GNU Parted. Disk /dev/sdf: 3000.6 GB, 3000592982016 bytes 255 heads, 63 sectors/track, 364801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000 Device Boot Start End Blocks Id System /dev/sdf1 1 267350 2147483647+ ee GPT Partition 1 does not start on physical sector boundary. WARNING: GPT (GUID Partition Table) detected on '/dev/sde'! The util fdisk doesn't support GPT. Use GNU Parted. Disk /dev/sde: 3000.6 GB, 3000592982016 bytes 255 heads, 63 sectors/track, 364801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000 Device Boot Start End Blocks Id System /dev/sde1 1 267350 2147483647+ ee GPT Partition 1 does not start on physical sector boundary. Usually it tells me which ones arn't partitioned and stuff, and I only have 6 drives in my server and there's 6 showing up here so I'm only assuming the first ones already mounted and formatted correctly? I'm not really sure if anyone would help me out here. Basically I just want to format and mount these drives :)

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  • error C2109: subscript requires array or pointer type

    - by numerical25
    I am trying to debug some homework but I am having trouble with these lines of code #include "stdafx.h" #include<conio.h> #include<iostream> #include<string> using namespace std; int main() { char word; cout << "Enter a word and I will tell you whether it is" << endl << "in the first or last half of the alphabet." << endl << "Please begin the word with a lowercase letter. --> "; cin >> word; if(word[0] >= 'm') cout << word << " is in the first half of the alphabet" << endl; else cout << word << " is in the last half of the alphabet" << endl; return 0; } I get the following error and I have no clue what its sayings error C2109: subscript requires array or pointer type

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  • MSWord automation:Get file contents after it was saved

    - by BlackTigerX
    I have an application that uses MSWord automation to edit some documents, after they save and close word I need to grab the modified file and put it back on the repository, there is only one scenario where I can't get it to work and that is when the user makes changes to the file, selects to close word and selects yes to save the file there are 2 events that I'm using: DocumentBeforeSave Quit on the Quit event I'm trying to load the .docx file from disk but on this particular scenario I get an IOException because the file is still in use, somehow I need to wait until after the Quit event has been processed, which is when Word is actually closed and the file is no longer being used right now I have it working using this word.Visible = true; while (!wordDone) { //gets changed to true on the Quit event System.Threading.Thread.Sleep(100); } bool error = false; do { try { //need to load the contents of the modified file ls.Content = System.IO.File.ReadAllBytes(provider.GetFileName()); error = false; } catch (System.IO.IOException) { error = true; System.Threading.Thread.Sleep(200); } } while (error); while this works it is very ugly, I need a way to fire an event after the Quit event has been handled, or block the current thread while word is still running, or get an event after the document has been saved, the bottom line is I need a clean way to load the file after it has been saved and word is closed. DocumentAfterSave would be awesome, but doesn't seem to exist. I Also tried unhooking the Quit handler and calling word.Quit on the Quit handler, that made no difference

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  • NSURLConnection and empty post variables

    - by SooDesuNe
    I'm at my wits end with this one, because I've used very similar code in the past, and it worked just fine. The following code results in empty $_POST variables on the server. I verified this with: file_put_contents('log_file_name', "log: ".$word, FILE_APPEND); the only contents of log_file_name was "log: " I then verified the PHP with a simple HTML form. It performed as expected. The Objective-C: NSString *word = "this_word_gets_lost"; NSString *myRequestString = [NSString stringWithFormat:@"word=%@", word]; [self postAsynchronousPHPRequest:myRequestString toPage:@"http://www.mysite.com/mypage.php" delegate:nil]; } -(void) postAsynchronousPHPRequest:(NSString*)request toPage:(NSString*)URL delegate:(id)delegate{ NSData *requestData = [ NSData dataWithBytes: [ request UTF8String ] length: [ request length ] ]; NSMutableURLRequest *URLrequest = [ [ NSMutableURLRequest alloc ] initWithURL: [ NSURL URLWithString: URL ] ]; [ URLrequest setHTTPMethod: @"POST" ]; [ URLrequest setHTTPBody: requestData ]; [ NSURLConnection connectionWithRequest:URLrequest delegate:delegate]; [URLrequest release]; } The PHP: $word = $_POST['word']; file_put_contents('log_file_name', "log: ".$word, FILE_APPEND); What am I doing wrong in the Objective-C that would cause the $_POST variable to be empty on the server?

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  • How do I get Bison/YACC to not recognize a command until it parses the whole string?

    - by chucknelson
    I have some bison grammar: input: /* empty */ | input command ; command: builtin | external ; builtin: CD { printf("Changing to home directory...\n"); } | CD WORD printf("Changing to directroy %s\n", $2); } ; I'm wondering how I get Bison to not accept (YYACCEPT?) something as a command until it reads ALL of the input. So I can have all these rules below that use recursion or whatever to build things up, which either results in a valid command or something that's not going to work. One simple test I'm doing with the code above is just entering "cd mydir mydir". Bison parses CD and WORD and goes "hey! this is a command, put it to the top!". Then the next token it finds is just WORD, which has no rule, and then it reports an error. I want it to read the whole line and realize CD WORD WORD is not a rule, and then report an error. I think I'm missing something obvious and would greatly appreciate any help - thanks! Also - I've tried using input command NEWLINE or something similar, but it still pushes CD WORD to the top as a command and then parses the extra WORD separately.

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  • How to map a Dictionary<string, string> spanning several tables

    - by Kim Johansson
    I have four tables: CREATE TABLE [Languages] ( [Id] INTEGER IDENTITY(1,1) NOT NULL, [Code] NVARCHAR(10) NOT NULL, PRIMARY KEY ([Id]), UNIQUE INDEX ([Code]) ); CREATE TABLE [Words] ( [Id] INTEGER IDENTITY(1,1) NOT NULL, PRIMARY KEY ([Id]) ); CREATE TABLE [WordTranslations] ( [Id] INTEGER IDENTITY(1,1) NOT NULL, [Value] NVARCHAR(100) NOT NULL, [Word] INTEGER NOT NULL, [Language] INTEGER NOT NULL, PRIMARY KEY ([Id]), FOREIGN KEY ([Word]) REFERENCES [Words] ([Id]), FOREIGN KEY ([Language]) REFERENCES [Languages] ([Id]) ); CREATE TABLE [Categories] ( [Id] INTEGER IDENTITY(1,1) NOT NULL, [Word] INTEGER NOT NULL, PRIMARY KEY ([Id]), FOREIGN KEY ([Word]) REFERENCES [Words] ([Id]) ); So you get the name of a Category via the Word - WordTranslation - Language relations. Like this: SELECT TOP 1 wt.Value FROM [Categories] AS c LEFT JOIN [WordTranslations] AS wt ON c.Word = wt.Word WHERE wt.Language = ( SELECT TOP 1 l.Id FROM [Languages] WHERE l.[Code] = N'en-US' ) AND c.Id = 1; That would return the en-US translation of the Category with Id = 1. My question is how to map this using the following class: public class Category { public virtual int Id { get; set; } public virtual IDictionary<string, string> Translations { get; set; } } Getting the same as the SQL query above would be: Category category = session.Get<Category>(1); string name = category.Translations["en-US"]; And "name" would now contain the Category's name in en-US. Category is mapped against the Categories table. How would you do this and is it even possible?

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  • Naive Bayesian classification (spam filtering) - Doubt in one calculation? Which one is right? Plz c

    - by Microkernel
    Hi guys, I am implementing Naive Bayesian classifier for spam filtering. I have doubt on some calculation. Please clarify me what to do. Here is my question. In this method, you have to calculate P(S|W) - Probability that Message is spam given word W occurs in it. P(W|S) - Probability that word W occurs in a spam message. P(W|H) - Probability that word W occurs in a Ham message. So to calculate P(W|S), should I do (1) (Number of times W occuring in spam)/(total number of times W occurs in all the messages) OR (2) (Number of times word W occurs in Spam)/(Total number of words in the spam message) So, to calculate P(W|S), should I do (1) or (2)? (I thought it to be (2), but I am not sure, so plz clarify me) I am refering http://en.wikipedia.org/wiki/Bayesian_spam_filtering for the info by the way. I got to complete the implementation by this weekend :( Thanks and regards, MicroKernel :) @sth: Hmm... Shouldn't repeated occurrence of word 'W' increase a message's spam score? In the your approach it wouldn't, right?. Lets take a scenario and discuss... Lets say, we have 100 training messages, out of which 50 are spam and 50 are Ham. and say word_count of each message = 100. And lets say, in spam messages word W occurs 5 times in each message and word W occurs 1 time in Ham message. So total number of times W occuring in all the spam message = 5*50 = 250 times. And total number of times W occuring in all Ham messages = 1*50 = 50 times. Total occurance of W in all of the training messages = (250+50) = 300 times. So, in this scenario, how do u calculate P(W|S) and P(W|H) ? Naturally we should expect, P(W|S) P(W|H)??? right. Please share your thought...

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  • When does the call() method get called in a Java Executor using Callable objects?

    - by MalcomTucker
    This is some sample code from an example. What I need to know is when call() gets called on the callable? What triggers it? public class CallableExample { public static class WordLengthCallable implements Callable { private String word; public WordLengthCallable(String word) { this.word = word; } public Integer call() { return Integer.valueOf(word.length()); } } public static void main(String args[]) throws Exception { ExecutorService pool = Executors.newFixedThreadPool(3); Set<Future<Integer>> set = new HashSet<Future<Integer>>(); for (String word: args) { Callable<Integer> callable = new WordLengthCallable(word); Future<Integer> future = pool.submit(callable); //**DOES THIS CALL call()?** set.add(future); } int sum = 0; for (Future<Integer> future : set) { sum += future.get();//**OR DOES THIS CALL call()?** } System.out.printf("The sum of lengths is %s%n", sum); System.exit(sum); } }

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  • How do you search a document for a string in c++?

    - by Jeff
    Here's my code so far: #include<iostream> #include<string> #include<fstream> using namespace std; int main() { int count = 0; string fileName; string keyWord; string word; cout << "Please make sure the document is in the same file as the program, thank you!" << endl << "Please input document name: " ; getline(cin, fileName); cout << endl; cout << "Please input the word you'd like to search for: " << endl; cin >> keyWord; cout << endl; ifstream infile(fileName.c_str()); while(infile.is_open()) { getline(cin,word); if(word == keyWord) { cout << word << endl; count++; } if(infile.eof()) { infile.close(); } } cout << count; } I'm not sure how to go to the next word, currently this infinite loops...any recommendation? Also...how do I tell it to print out the line that that word was on? Thanks in advance!

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  • Letting user carry on after three attempts

    - by sMilbz
    In my spelling game there is a grid that is populated with words. The words are hidden and the aim of the game is to spell the word that is highlighted with the aid of a sound and a picture. To highlight a word you press the "next" button. At the moment if you spell the word correctly it says "well done" and you can advance to the next word, but if you spell it incorrectly you have to keep attempting the word until it is complete. As the game is designed for children I do not think this is the best approach, so I would like to make it so you can advance after 3 incorrect attempts. I have played around with the script so much trying to put counters on incorrect attempts and then making the button active but cannot seem to get it to work. Can someone please help me? Here is the script for the button var noExist = $('td[data-word=' + listOfWords[rndWord].name + ']').hasClass('wordglow2'); if (noExist) { $('.minibutton').click(); } else { $('.minibutton').click('disable'); $("#mysoundclip").attr('src', listOfWords[rndWord].audio); audio.play(); $("#mypic").attr('src', listOfWords[rndWord].pic); pic.show(); } }); "wordglow2" is the style applied if the word is spelt correctly. Here is a fiddle to help understand... http://jsfiddle.net/smilburn/ZAfVZ/4/

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  • Parsing text files

    - by d03boy
    I encountered a situation tonight where I wanted to parse a text file. I had a very, very long word list that contained English words delimited by lines. I wanted to get rid of every word (or line) that was longer than 7 characters. This would be simple in Linux but I can't seem to find a simple solution in WindowsXP. I tried using Notepad++ regular expression search but that was a huge failure. I tried using the expression .{6,} without finding any matches. I'm really at a loss because I thought this sort of thing would be extremely easy and there would be tons of tools to accomplish a task like this. It seems like Notepad++ supports every other feature in the world except the very basic ones that seem the most obvious. Another one of my goals was to put some code before and after the word on each line. aardvark apple azolio would turn into INSERT INTO Words (word) VALUES ('aardvark'); INSERT INTO Words (word) VALUES ('apple'); INSERT INTO Words (word) VALUES ('azolio'); What suggestions/tools/tips do you have to accomplish tasks similar to this in WindowsXP?

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  • HP Laserjet 1320 drivers for Windows 7

    - by RedGrittyBrick
    Background I replaced som XP computers with Win 7 computers. We have a HP Laserjet 1320dn printer attached to the LAN. The XP computers could print to it from Word in duplex mode without any issues. Problem The Win 7 computers downloaded a full set of drivers including a "HP Laserjet 1320 PCL5" driver. However using this, Word's page footers cause extra pages to be printed with just a letter or so at a time from the footer. Some other apps have similar issues. I also have an ancient Laserjet 1200 attached to the LAN via a Jetdirect box and that works just fine. So I don't think the problem is with Word (the computers came with Word 2010 starter). What I tried I wrangled the control-panel new printer dialogue into using a "HP Laserjet 2100 PS" driver for the HP Laserjet 1320dn. Now my Word documents print as they should. However I don't have a duplex option on the print dialogue. I'd really like to be able to use duplex printing. Question Windows used to have a Universal Postscript driver that read a Postscript Printer Definition (PPD) file to make the printer's features available (tray choice, duplex etc). I can't see any way to do this in Windows 7. Is there a way? Is there any other way I can get Windows 7 Home Premium 64-bit to print properly to a HP Laserjet 1320dn and have access to all it's major features? Addendum: My page in Word looks like this: +--------------------+ | aa bb cc | | | | lorem ipsum dolor | | | ... | | | pp qq rr | +--------------------+ The headers and footers were inserted using Insert - header - blank (3 column). When printed I get 1 page with aa, bb, cc, pp in correct position (no other text) 1 blank page 1 page with qq in correct position (no other text) 1 blank page 1 page with rr in correct position (no other text) 1 blank page 1 page with lorem ipsum dolor in correct position (no headers or footers) If I use a Laserjet 2100 driver I get 1 correct page.

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  • Why are cookies unrecognized when a link is clicked from an external source (i.e. Excel, Word, etc..

    - by Nick
    I noticed that when a link is clicked externally from the web browser, such as from Excel or Word, that my session cookie is initially unrecognized, even if the link opens up in a new tab of the same browser window. The browser ends up recognizing its cookie eventually, but I am puzzled as to why that initial link from Excel or Word doesn't work. To make it even more challenging, clicking a link works fine from Outlook. Does anybody know why this might be happening? I'm using the Zend Framework with PHP 5.3.

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • sed + RE , want to ignore remarked line using sed

    - by yael
    I want to replace the a string with the word string as the following example down , but if a string exist also after comment then a string will replaced too In which way I can add to the sed command the irregular exp that ignore from the #. [root@localhost tmp]# more test a b aa bb #a #b #aa #bb [root@localhost tmp]# sed "/\/ s/a/WORD/g" test WORD b aa bb #WORD #b #aa #bb [root@localhost tmp]#

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  • Issues with MIPS interrupt for tv remote simulator

    - by pred2040
    Hello I am writing a program for class to simulate a tv remote in a MIPS/SPIM enviroment. The functions of the program itself are unimportant as they worked fine before the interrupt so I left them all out. The gaol is basically to get a input from the keyboard by means of interupt, store it in $s7 and process it. The interrupt is causing my program to repeatedly spam the errors: Exception occurred at PC=0x00400068 Bad address in data/stack read: 0x00000004 Exception occurred at PC=0x00400358 Bad address in data/stack read: 0x00000000 program starts here .data msg_tvworking: .asciiz "tv is working\n" msg_sec: .asciiz "sec -- " msg_on: .asciiz "Power On" msg_off: .asciiz "Power Off" msg_channel: .asciiz " Channel " msg_volume: .asciiz " Volume " msg_sleep: .asciiz " Sleep Timer: " msg_dash: .asciiz "-\n" msg_newline: .asciiz "\n" msg_comma: .asciiz ", " array1: .space 400 # 400 bytes of storage for 100 channels array2: .space 400 # copy of above for sorting var1: .word 0 # 1 if 0-9 is pressed, 0 if not var2: .word 0 # stores number of channel (ex. 2-) var3: .word 0 # channel timer var4: .word 0 # 1 if s pressed once, 2 if twice, 0 if not var5: .word 0 # sleep wait timer var6: .word 0 # program timer var9: .float 0.01 # for channel timings .kdata var7: .word 10 var8: .word 11 .text .globl main main: li $s0, 300 li $s1, 0 # channel li $s2, 50 # volume li $s3, 1 # power - 1:on 0:off li $s4, 0 # sleep timer - 0:off li $s5, 0 # temporary li $s6, 0 # length of sleep period li $s7, 10000 # current key press li $t2, 0 # temp value not needed across calls li $t4, 0 interrupt data here mfc0 $a0, $12 ori $a0, 0xff11 mtc0 $a0, $12 lui $t0, 0xFFFF ori $a0, $0, 2 sw $a0, 0($t0) mainloop: # 1. get external input, and process it # input from interupt is taken from $a2 and placed in $s7 #for processing beq $a2, $0, next lw $s7, 4($a2) li $a2, 0 # call the process_input function here # jal process_input next: # 2. check sleep timer mainloopnext1: # 3. delay for 10ms jal delay_10ms jal check_timers jal channel_time # 4. print status lw $s5, var6 addi $s5, $s5, 1 sw $s5, var6 addi $s0, $s0, -1 bne $s0, $0, mainloopnext4 li $s0, 300 jal status_print mainloopnext4: j mainloop li $v0,10 # exit syscall -------------------------------------------------- status_print: seconds_stat: power_stat: on_stat: off_stat: channel_stat: volume_stat: sleep_stat: j $ra -------------------------------------------------- delay_10ms: li $t0, 6000 delay_10ms_loop: addi $t0, $t0, -1 bne $t0, $0, delay_10ms_loop jr $ra -------------------------------------------------- check_timers: channel_press: sleep_press: go_back_press: channel_check: channel_ignore: sleep_check: sleep_ignore: j $ra ------------------------------------------------ process_input: beq $s7, 112, power beq $s7, 117, channel_up beq $s7, 100, channel_down beq $s7, 108, volume_up beq $s7, 107, volume_down beq $s7, 115, sleep_init beq $s7, 118, history bgt $s7, 47, end_range jr $ra end_range: power: on: off: channel_up: over: channel_down: under: channel_message: channel_time: volume_up: volume_down: volume_message: sleep_init: sleep_incr: sleep: sleep_reset: history: digit_pad_init: digit_pad: jr $ra -------------------------------------------- interupt data here, followed closely from class .ktext 0x80000180 .set noat move $k1, $at .set at sw $v0, var7 sw $a0, var8 mfc0 $k0, $13 srl $a0, $k0, 2 andi $a0, $a0, 0x1f bne $a0, $zero, no_io lui $v0, 0xFFFF lw $a2, 4($v0) # keyboard data placed in $a2 no_io: mtc0 $0, $13 mfc0 $k0, $12 andi $k0, 0xfffd ori $k0, 0x11 mtc0 $k0, $12 lw $v0, var7 lw $a0, var8 .set noat move $at, $k1 .set at eret Thanks in advance.

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  • Hotkey for double-click highlight?

    - by Steven Wright
    I'm working in Eclipse and find myself always replacing multiple copies of the same word, but I always have to take my hands off the keyboard and screen to get the mouse, hover over the word, double click to select, and then copy or rewrite the word. Is there any way I can just move the cursor inside the word and hit some hotkey that would highlight it? Seems like this would be a big timesaver. Or if there's a way to create a hotkey that would be perfect too.

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  • Bash: trim a parameter from both ends

    - by Andrey Kazak
    Greetings! This are well know Bash parameter expansion patterns: ${parameter#word}, ${parameter##word} and ${parameter%word}, ${parameter%%word} I need to chop one part from the beginning and anoter part from the trailing of the parameter. Could you advice something for me please?

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  • C# Spell checker Problem

    - by reggie
    I've incorporated spell check into my win forms C# project. This is my code. public void CheckSpelling() { try { // declare local variables to track error count // and information int SpellingErrors = 0; string ErrorCountMessage = string.Empty; // create an instance of a word application Microsoft.Office.Interop.Word.Application WordApp = new Microsoft.Office.Interop.Word.Application(); // hide the MS Word document during the spellcheck //WordApp.WindowState = WdWindowState.wdWindowStateMinimize; // check for zero length content in text area if (this.Text.Length > 0) { WordApp.Visible = false; // create an instance of a word document _Document WordDoc = WordApp.Documents.Add(ref emptyItem, ref emptyItem, ref emptyItem, ref oFalse); // load the content written into the word doc WordDoc.Words.First.InsertBefore(this.Text); // collect errors form new temporary document set to contain // the content of this control Microsoft.Office.Interop.Word.ProofreadingErrors docErrors = WordDoc.SpellingErrors; SpellingErrors = docErrors.Count; // execute spell check; assumes no custom dictionaries WordDoc.CheckSpelling(ref oNothing, ref oIgnoreUpperCase, ref oAlwaysSuggest, ref oNothing, ref oNothing, ref oNothing, ref oNothing, ref oNothing, ref oNothing, ref oNothing, ref oNothing, ref oNothing); // format a string to contain a report of the errors detected ErrorCountMessage = "Spell check complete; errors detected: " + SpellingErrors; // return corrected text to control's text area object first = 0; object last = WordDoc.Characters.Count - 1; this.Text = WordDoc.Range(ref first, ref last).Text; } else { // if nothing was typed into the control, abort and inform user ErrorCountMessage = "Unable to spell check an empty text box."; } WordApp.Quit(ref oFalse, ref emptyItem, ref emptyItem); System.Runtime.InteropServices.Marshal.ReleaseComObject(WordApp); // return report on errors corrected // - could either display from the control or change this to // - return a string which the caller could use as desired. // MessageBox.Show(ErrorCountMessage, "Finished Spelling Check"); } catch (Exception e) { MessageBox.Show(e.ToString()); } } The spell checker works well, the only problem is when I try to move the spell checker the main form blurs up for some reason. Also when I close the spell checker the main form is back to normal. It seems like it is opening up Microsoft word then hiding the window, only allowing the spell checker to be seen. Please help.

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  • Regular Expression question

    - by Mohammad Kotb
    Hi, In my academic assignment, I want make a regular expression to match a word with the following specifications: word length greater than or equal 1 and less than or equal 8 contains letters, digits, and underscore first digit is a letter only word is not A,X,S,T or PC,SW I tried for this regex but can't continue (My big problem is to make the word not equal to PC and SW) ([a-zA-Z&&[^AXST]])|([a-zA-Z][\w]{0,7}) But in the previous regex I didn't handle the that it is not PC and SW Thanks,

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  • Split comma separated string to count duplicates

    - by josepv
    I have the following data in my database (comma separated strings): "word, test, hello" "test, lorem, word" "test" ... etc How can I transform this data into a Dictionary whereby each string is separated into each distinct word together with the number of times that it occurs, i.e. {"test", 3}, {"word", 2}, {"hello", 1}, {"lorem", 1} I will have approximately 3000 rows of data in case this makes a difference to any solution offered. Also I am using .NET 3.5 (and would be interested to see any solution using linq)

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  • Modify a php limit text function adding some kind of offset to it

    - by webmasters
    Maybe you guys can help: I have a variable called $bio with bio data. $bio = "Hello, I am John, I'm 25, I like fast cars and boats. I work as a blogger and I'm way cooler then the author of the question"; I search the $bio using a set of functions to search for a certain word, lets say "author" which adds a span class around that word, and I get: $bio = "Hello, I am John, I'm 25, I like fast cars and boats. I work as a blogger and I'm way cooler then the <span class=\"highlight\">author</span> of the question"; I use a function to limit the text to 85 chars: $bio = limit_text($bio,85); The problem is when there are more then 80 chars before the word "author" in $bio. When the limit_text() is applied, I won't see the highlighted word author. What I need is for the limit_text() function to work as normal, adding all the words that contain the span class highlight at the end. Something like this: *"This is the limited text to 85 chars, but there are no words with the span class highlight so I am putting to be continued ... **author**, **author2** (and all the other words that have a span class highlight around them separate by comma "* Hope you understood what I mean, if not, please comment and I'll try to explain better. Here is my limit_text() function: function limit_text($text, $length){ // Limit Text if(strlen($text) > $length) { $stringCut = substr($text, 0, $length); $text = substr($stringCut, 0, strrpos($stringCut, ' ')); } return $text; } UPDATE: $xturnons = str_replace(",", ", ", $xturnons); $xbio = str_replace(",", ", ", $xbio); $xbio = customHighlights($xbio,$toHighlight); $xturnons = customHighlights($xturnons,$toHighlight); $xbio = limit_text($xbio,85); $xturnons = limit_text($xturnons,85); The customHighlights function which adds the span class highlighted: function addRegEx($word){ // Highlight Words return "/" . $word . '[^ ,\,,.,?,\.]*/i'; } function highlight($word){ return "<span class='highlighted'>".$word[0]."</span>"; } function customHighlights($searchString,$toHighlight){ $searchFor = array_map('addRegEx',$toHighlight); $result = preg_replace_callback($searchFor,'highlight',$searchString); return $result; }

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  • Approximate timings for various operations on a "typical desktop PC" anno 2010

    - by knorv
    In the article "Teach Yourself Programming in Ten Years" Peter Norvig (Director of Research, Google) gives the following approximate timings for various operations on a typical 1GHz PC back in 2001: execute single instruction = 1 nanosec = (1/1,000,000,000) sec fetch word from L1 cache memory = 2 nanosec fetch word from main memory = 10 nanosec fetch word from consecutive disk location = 200 nanosec fetch word from new disk location (seek) = 8,000,000 nanosec = 8 millisec What would the corresponding timings be for your definition of a typical PC desktop anno 2010?

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