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  • GWT - Retrieve size of a widget that is not displayed

    - by Garagos
    I need to set the size of an absolutePanel regarding to its child size, but the getOffset* methods return 0 because (i think) the child as not been displayed yet. A Quick example: AbsolutePanel aPanel = new AbsolutePanel(); HTML text = new HTML(/*variable lenght text*/); int xPosition = 20; // actually variable aPanel.add(text, xPosition, 0); aPanel.setSize(xPosition + text .getOffsetWidth() + "px", "50px"); // 20px 50px I could also solve my problem by using the AbsolutePanel size to set the child position and size: AbsolutePanel aPanel = new AbsolutePanel(); aPanel.setSize("100%", "50px"); HTML text = new HTML(/*variable lenght text*/); int xPosition = aPanel.getOffsetWidth() / 3; // Once again, getOffsetWidth() returns 0; aPanel.add(text, xPosition, 0); In both case, i have to find a way to either: retrieve the size of a widget that has not been displayed be notified when a widget is displayed

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  • Function in xcode

    - by Joy
    I have a function which have two global variable 1.temp-a nsmutable array 2.j-a int type variable. But i cant access any global variable inside this function. I'm giving the code sample. void print( NSArray *array) { NSEnumerator *enumerator = [array objectEnumerator]; id obj; while ( nil!=(obj = [enumerator nextObject]) ) { NSString *tem=[[obj description] cString]; [temp insertObject:tem atIndex:j]; j=j+1; printf( "%s\n", [[obj description] cString]); } } Looking forward to your response. Thanks in advance..

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  • AppEngine: Can I write a Dynamic property (db.Expando) with a name chosen at runtime?

    - by MarcoB
    If I have an entity derived from db.Expando I can write Dynamic property by just assigning a value to a new property, e.g. "y" in this example: class MyEntity(db.Expando): x = db.IntegerProperty() my_entity = MyEntity(x=1) my_entity.y = 2 But suppose I have the name of the dynamic property in a variable... how can I (1) read and write to it, and (2) check if the Dynamic variable exists in the entity's instance? e.g. class MyEntity(db.Expando): x = db.IntegerProperty() my_entity = MyEntity(x=1) # choose a var name: var_name = "z" # assign a value to the Dynamic variable whose name is in var_name: my_entity.property_by_name[var_name] = 2 # also, check if such a property esists if my_entity.property_exists(var_name): # read the value of the Dynamic property whose name is in var_name print my_entity.property_by_name[var_name] Thanks...

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  • How can I create an enum using numbers?

    - by Jordan S
    Is it possible to make an enum using just numbers in C#? In my program I have a variable, Gain, that can only be set to 1, 2, 4, and 8. I am using a propertygrid control to display and set this value. If I were to create an enum like this... private enum GainValues {One, Two, Four, Eight} and I made my gain variable of type GainValues then the drop-down list in the propertygrid would only show the available values for the gain variable. The problem is I want the gain values to read numerically an not as words. But I can not create an enum like this: private enum GainValues {1,2,4,8} So is there another way of doing this? Perhaps creating a custom type?

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  • A Tkinter StringVar() Question

    - by Graham
    I would like to create a StringVar() that looks something like this: someText = "The Spanish Inquisition" #Here's a normal variable whose value I will change eventually TkEquivalent = StringVar() #and here's the StringVar() TkEquivalent.set(string(someText)) #and here I set it equal to the normal variable. When someText changes, this variable will too... HOWEVER: TkEquivalent.set("Nobody Expects " + string(someText)) If I do this, the StringVar() will no longer automatically update! How can I include that static text and still have the StringVar() update to reflect changes made to someText? Thanks for your help.

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  • Does this make any sense (Apple-documentation)?

    - by Paperflyer
    Here is a snippet of the official Apple Documentation of AudioBufferList (Core Audio Data Types Reference) AudioBufferList Holds a variable length array of AudioBuffer structures. struct AudioBufferList { UInt32 mNumberBuffers; AudioBuffer mBuffers[1]; }; typedef struct AudioBufferList AudioBufferList; Fields mNumberBuffers The number of AudioBuffer structures in the mBuffers array. mBuffers A variable length array of AudioBuffer structures. If mBuffers is defined as AudioBuffer[1] it is not of variable length and thus mNumberBuffers is implicitly defined as 1. Do I miss something here or is this just nonsense?

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  • Can a programming language without arrays be turing-complete?

    - by Ring
    My question is simple: There are no arrays possible. That means you can address variables only "statically" by directly using their unique name. (This already throws out the default array syntax variable[ index ] and variable variables) "Emulated arrays" are counted as arrays and excluded too. Examples: You could basically simulate arrays using strings (quite easily actually) or use variable variables as in PHP. Can such a language be turing-complete? Brainf*ck for example has arrays, in fact it is one big array, isn't it?

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  • Python Class Variables Question

    - by zyq524
    I have some doubt about python's class variables. As my understanding, if I define a class variable, which is declared outside the init() function, this variable will create only once as a static variable in C++. This seems right for some python types, for instance, dict and list type, but for those base type, e.g. int,float, is not the same. For example: class A: dict1={} list1=list() int1=3 def add_stuff(self, k, v): self.dict1[k]=v self.list1.append(k) self.int1=k def print_stuff(self): print self.dict1,self.list1,self.int1 a1 = A() a1.add_stuff(1, 2) a1.print_stuff() a2=A() a2.print_stuff() The output is: {1: 2} [1] 1 {1: 2} [1] 3 I understand the results of dict1 and list1, but why does int1 behavior different?

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  • Read data from specific memory address

    - by rapid
    Hello. How can I read (and put into new variable) data stored at specific memory address? For instance I know that: <nfqueue.queue; proxy of <Swig Object of type 'queue *' at 0xabd2b00> > And I want to have data stored at 0xabd2b00 in new variable so that I can work and use all functionalities of the object. Let's assume that I don't have access to the original variable that created this object.

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  • Double # showing 0 on android

    - by Dave
    I'm embarrassed to ask this question, but after 45 minutes of not finding a solution I will resort to public humiliation. I have a number that is being divided by another number and I'm storing that number in a double variable. The numbers are randomly generated, but debugging the app shows that both numbers are in fact being generated. Lets just say the numbers are 476 & 733. I then take the numbers and divide them to get the percentage 476/733 = .64 I then print out the variable and it's always set to 0. I've tried using DecimalFormat and NumberFormat. No matter what I try though it always says the variable is 0. I know there is something simple that I'm missing, I just can't find it =/.

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  • Within SSIS - Is it possible to deploy one package multiple times in the same instance and set diffe

    - by Matt
    In my environment my Dev and QA Database Instances are on the same server. I would like to deploy the same package (or different versions of the package) into SSIS and set the filter to select different rows in the Config table. Is this possible? This is SQL 2005. For the sake of this question lets say I have one variable, which is a directory path. I would like to have these variables in the table twice (with different Filters applied (Dev and QA) as below (simplified) . . . Filter / Variable Value / Variable Name Dev / c:\data\dev / FilePath QA / c:\data\qa / FilePath Do I need to apply a change within the settings of the package in SSIS or is it changed on the job step within Agent? Any help would be appreciated.

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  • a macro question for c language (#define)

    - by Daniel
    I am reading source code of hoard memory allocator, and in the file of gnuwrapper.cpp, there are the following code #define CUSTOM_MALLOC(x) CUSTOM_PREFIX(malloc)(x) What's the meaning of CUSTOM_PREFIX(malloc)(x)? is CUSTOM_PREFIX a function? But as a function it didn't defined anywhere. If it's variable, then how can we use variable like var(malloc)(x)? more code: #ifndef __GNUC__ #error "This file requires the GNU compiler." #endif #include <string.h> #include <stdlib.h> #include <stdio.h> #include <malloc.h> #ifndef CUSTOM_PREFIX ==> here looks like it's a variable, so if it doesn't define, then define here. #define CUSTOM_PREFIX #endif #define CUSTOM_MALLOC(x) CUSTOM_PREFIX(malloc)(x) ===> what's the meaning of this? #define CUSTOM_FREE(x) CUSTOM_PREFIX(free)(x) #define CUSTOM_REALLOC(x,y) CUSTOM_PREFIX(realloc)(x,y) #define CUSTOM_MEMALIGN(x,y) CUSTOM_PREFIX(memalign)(x,y)

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  • How do you pass objects between View Controllers in Objective-C?

    - by editor
    I've been trudging through some code for two days trying to figure out why I couldn't fetch a global NSMutableArray variable I declared in the .h and implemented in .m and set in a the viewDidLoad function. It finally dawned on me: there's no such thing as a global variable in Objective-C, at least not in the PHP sense I've come to know. I didn't ever really read the XCode error warnings, but there it was, even if not quite plain English: "Instance variable 'blah' accessed in class method." My question: What am I supposed to do now? I've got two View Controllers that need to access a central NSMutableDictionary I generate from a JSON file via URL. It's basically an extended menu for all my Table View drill downs, and I'd like to have couple other "global" (non-static) variables. Do I have to grab the JSON each time I want to generate this NSMutableDictionary or is there some way to set it once and access it from various classes via #import? Do I have to write data to a file, or is there another way people usually do this?

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  • Guidance for Php for a beginner

    - by luckyluke
    I've just started to learn PHP. I found the $_POST variable is not working and posted the same at the below link $_POST[] not working in php and as per the advise i installed XAMPP. But still the proble of $_POST variable is not solved. Now i've a doubt whether i need to configure any global variable to make $_POST work. I'm totally lost on this and dont know how to proceed. Any help on this is verryy much appreciated. Thanks.

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  • scope of variables java

    - by qxc
    Is a variable inside the main, a public variable? public static void main(String[] args) { ......... for(int i=0;i<threads.length;i++) try { threads[i].join(); } catch (InterruptedException e) { e.printStackTrace(); } long time=0; .... } i and time are they both public variables? Of course if my reasoning is correct, also any variable belonging to a public method should be considered public.. am i right? Thanks

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  • Make array from $_POST values

    - by cbarg
    Let's start telling that I'm passing an x amount of variables via post from a form. Let's name them menu_category_1, menu_category_2, ..., menu_category_x, plus, maybe, menu_category_new (I'm using an if empty to check this last one variable). To make things easier I'm also sending the parameter $key (amount of variables starting from 0). Now I need to set them into a new variable $menu_category (array), which is going to be imploded and then update my database. How do I set up that new $menu_category variable to be an array containing all my variables named in the beginning? I was thinking of using a for loop but I can't come up with something useful. Thanks!!!

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  • Quite confused about what constitutes Current state of a resource

    - by bckpwrld
    From REST in Practice: Hypermedia and Systems Architecture: The current state of a resource is a combination of: The values of information items belonging to that resource Links to related resources Links that represent a transition to a possible future state of the current resource The results of evaluating any business rules that relate the resource to other local resources a) why would "links to related resources" also represent the current state of a resource? b) I also don't quite understand why "Links that represent a transition to a possible future state of the current resource" also represent the the current state. Namely, those links represent the possibility, not the current state. Analogy would be an int variable set to value 10. It's possible that in the future this variable will get processed and set to value 100, but we don't claim its current state also includes possible future state of 100?! thank you

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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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  • VSTO Troubleshooting Quick Tips

    - by João Angelo
    If you ever find yourself troubleshooting a VSTO addin that does not load then these steps will interest you. Do not skip the basics and check the registry at HKLM\Software\Microsoft\Office\<Application>\AddIns\<AddInName> or HKCU\Software\Microsoft\Office\<Product>\AddIns\<Application> because if the LoadBehavior key is not set to 3 the office application will not even try to load it on startup; Enable error alerts popups by configuring an environment variable SET VSTO_SUPPRESSDISPLAYALERTS=0 Enable logging errors to file by configuring an environment variable SET VSTO_LOGALERTS=1 Pray for an error alert popup or for an error in the log file so that you can fix its cause.  

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  • 10 CSS Grid Layout Generators

    - by Jyoti
    There are a lot of online generators which are of no use to any designers, however some can help designers to an extent. Some example of online generators are favicon generators, background generators, button generators, and badge generators. Some of the useful kinds are the ones that solve one purpose with quick and easy steps, especially useful for new designers, following is a list of some useful CSS grid layout generators. Grid Layout Generator By PageColumn: Blueprint Grid CSS Generator: Grid Generator By NetProtozo: Grid Generator By DegisnByGrid: Grid System Generator: YUI CSS Grid Builder: Variable Grid System: Firdamatic: CSS Sourced Ordered Variable Border Columed Page Maker: Grid Designer:

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  • BizTalk 2009 - Naming Guidelines

    - by StuartBrierley
    The following is effectively a repost of the BizTalk 2004 naming guidlines that I have previously detailed.  I have posted these again for completeness under BizTalk 2009 and to allow an element of separation in case I find some reason to amend these for BizTalk 2009. These guidlines should be universal across any version of BizTalk you may wish to apply them to. General Rules All names should be named with a Pascal convention. Project Namespaces For message schemas: [CompanyName].XML.Schemas.[FunctionalName]* Examples:  ABC.XML.Schemas.Underwriting DEF.XML.Schemas.MarshmellowTradingExchange * Donates potential for multiple levels of functional name, such as Underwriting.Dictionary.Valuation For web services: [CompanyName].Web.Services.[FunctionalName] Examples: ABC.Web.Services.OrderJellyBeans For the main BizTalk Projects: [CompanyName].BizTalk.[AssemblyType].[FunctionalName]* Examples: ABC.BizTalk.Mappings.Underwriting ABC.BizTalk.Orchestrations.Underwriting * Donates potential for multiple levels of functional name, such as Mappings.Underwriting.Valuations Assemblies BizTalk Assembly names should match the associated Project Namespace, such as ABC.BizTalk.Mappings.Underwriting. This pertains to the formal assembly name and the DLL name. The Solution name should take the name of the main project within the solution, and also therefore the namespace for that project. Although long names such as this can be unwieldy to work with, the benefits of having the full scope available when the assemblies are installed on the target server are generally judged to outweigh this inconvenience. Messaging Artifacts Artifact Standard Notes Example Schema <DescriptiveName>.xsd   .NET Type name should match, without file extension.    .NET Namespace will likely match assembly name. PurchaseOrderAcknowledge_FF.xsd  or FNMA100330_FF.xsd Property Schema <DescriptiveName>.xsd Should be named to reflect possible common usage across multiple schemas  IspecMessagePropertySchema.xsd UnderwritingOrchestrationKeys.xsd Map <SourceSchema>2<DestinationSchema>.btm Exceptions to this may be made where the source and destination schemas share the majority of the name, such as in mainframe web service maps InstructionResponse2CustomEmailRequest.btm (exception example) AccountCustomerAddressSummaryRequest2MainframeRequest.btm Orchestration <DescriptiveName>.odx   GetValuationReports.odx SendMTEDecisionResponse.odx Send/Receive Pipeline <DescriptiveName>.btp   ValidatingXMLReceivePipeline.btp FlatFileAssembler.btp Receive Port A plainly worded phrase that will clearly explain the function.    FraudPreventionServices LetterProcessing   Receive Location A plainly worded phrase that will clearly explain the function.  ? Do we want to include the transport type here ? Arrears Web Service Send Port Group A plainly worded phrase that will clearly explain the function.   Customer Updates Send Port A plainly worded phrase that will clearly explain the function.    ABCProductUpdater LogLendingPolicyOutput Parties A meaningful name for a Trading Partner. If dealing with multiple entities within a Trading Partner organization, the Organization name could be used as a prefix.   Roles A meaningful name for the role that a Trading Partner plays.     Orchestration Workflow Shapes Shape Standard Notes Example Scopes <DescriptionOfContainedWork> or <DescOfcontainedWork><TxType>   Including info about transaction type may be appropriate in some situations where it adds significant documentation value to the diagram. HandleReportResponse         Receive Receive<MessageName> Typically, MessageName will be the same as the name of the message variable that is being received “into”. ReceiveReportResponse Send Send<MessageName> Typically, MessageName will be the same as the name of the message variable that is being sent. SendValuationDetailsRequest Expression <DescriptionOfEffect> Expression shapes should be named to describe the net effect of the expression, similar to naming a method.  The exception to this is the case where the expression is interacting with an external .NET component to perform a function that overlaps with existing BizTalk functionality – use closest BizTalk shape for this case. CreatePrintXML Decide <DescriptionOfDecision> A description of what will be decided in the “if” branch Report Type? Perform MF Save? If-Branch <DescriptionOfDecision> A (potentially abbreviated) description of what is being decided Mortgage Valuation Yes Else-Branch Else Else-branch shapes should always be named “Else” Else Construct Message (Assign) Create<Message> (for Construct)     <ExpressionDescription> (for expression) If a Construct shape contains a message assignment, it should be prefixed with “Create” followed by an abbreviated name of the message being assigned.    The actual message assignment shape contained should be named to describe the expression that is contained. CreateReportDataMV   which contains expression: ExtractReportData Construct Message (Transform) Create<Message> (for Construct)   <SourceSchema>2<DestSchema> (for transform) If a Construct shape contains a message transform, it should be prefixed with “Create” followed by an abbreviated name of the message being assigned.   The actual message transform shape contained should generally be named the same as the called map.  CreateReportDataMV   which contains transform: ReportDataMV2ReportDataMV                 Construct Message (containing multiple shapes)   If a Construct Message shape uses multiple assignments or transforms, the overall shape should be named to communicate the net effect, using no prefix.     Call/Start Orchestration Call<OrchestrationName>   Start<OrchestrationName>     Throw Throw<ExceptionType> The corresponding variable name for the exception type should (often) be the same name as the exception type, only camel-cased. ThrowRuleException, which references the “ruleException” variable.     Parallel <DescriptionOfParallelWork> Parallel shapes should be named by a description of what work will be done in parallel   Delay <DescriptionOfWhatWaitingFor> Delay shapes should be named by a description of what is being waited for.  POAcknowledgeTimeout Listen <DescriptionOfOutcomes> Listen shapes should be named by a description that captures (to the degree possible) all the branches of the Listen shape POAckOrTimeout FirstShippingBid Loop <DescriptionOfLoop> A (potentially abbreviated) description of what the loop is. ForEachValuationReport WhileErrorFlagTrue Role Link   See “Roles” in messaging naming conventions above.   Suspend <ReasonDescription> Describe what action an administrator must take to resume the orchestration.  More detail can be passed to error property – and should include what should be done by the administrator before resuming the orchestration. ReEstablishCreditLink Terminate <ReasonDescription> Describe why the orchestration terminated.  More detail can be passed to error property. TimeoutsExpired Call Rules Call<PolicyName> The policy name may need to be abbreviated. CallLendingPolicy Compensate Compensate or Compensate<TxName> If the shape compensates nested transactions, names should be suffixed with the name of the nested transaction – otherwise it should simple be Compensate. CompensateTransferFunds Orchestration Types Type Standard Notes Example Multi-Part Message Types <LogicalDocumentType>   Multi-part types encapsulate multiple parts.  The WSDL spec indicates “parts are a flexible mechanism for describing the logical abstract content of a message.”  The name of the multi-part type should correspond to the “logical” document type, i.e. what the sum of the parts describes. InvoiceReceipt   (which might encapsulate an invoice acknowledgement and a payment voucher.) Multi-Part Messsage Part <SchemaNameOfPart> Should be named (most often) simply for the schema (or simple type) associated with the part. InvoiceHeader Messages <SchemaName> or <MuliPartMessageTypeName> Should be named based on the corresponding schema type or multi-part message type.  If there is more than one variable of a type, name for its use within the orchestration. ReportDataMV UpdatedReportDataMV Variables <DescriptiveName>   TargetFilePath StringProcessor Port Types <FunctionDescription>PortType Should be named to suggest the nature of an endpoint, with pascal casing and suffixed with “PortType”.   If there will be more than one Port for a Port Type, the Port Type should be named according to the abstract service supplied.   The WSDL spec indicates port types are “a named set of abstract operations and the abstract messages involved” that also encapsulates the message pattern (i.e. one-way, request-response, solicit-response) that all operations on the port type adhere to. ReceiveReportResponsePortType  or CallEAEPortType (This is a two way port, so Receove or Send alone would not be appropriate.  Could have been ProcessEAERequestPortType etc....) Ports <FunctionDescription>Port Should be named to suggest a grouping of functionality, with pascal casing and suffixed with “Port.”  ReceiveReportResponsePort CallEAEPort Correlation types <DescriptiveName> Should be named based on the logical name of what is being used to correlate.  PurchaseOrderNumber Correlation sets <DescriptiveName> Should be named based on the corresponding correlation type.  If there is more than one, it should be named to reflect its specific purpose within the orchestration.   PurchaseOrderNumber Orchestration parameters <DescriptiveName> Should be named to match the caller’s names for the corresponding variables where appropriate.

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  • Is it bad to have an "Obsessive Refactoring Disorder"?

    - by Rachel
    I was reading this question and realized that could almost be me. I am fairly OCD about refactoring someone else's code when I see that I can improve it. For example, if the code contains duplicate methods to do the same thing with nothing more than a single parameter changing, I feel I have to remove all the copy/paste methods and replace it with one generic one. Is this bad? Should I try and stop? I try not to refactor unless I can actually make improvements to the code performance or readability, or if the person who did the code isn't following our standard naming conventions (I hate expecting a variable to be local because of the naming standard, only to discover it is a global variable which has been incorrectly named)

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  • C++ Little Wonders: The C++11 auto keyword redux

    - by James Michael Hare
    I’ve decided to create a sub-series of my Little Wonders posts to focus on C++.  Just like their C# counterparts, these posts will focus on those features of the C++ language that can help improve code by making it easier to write and maintain.  The index of the C# Little Wonders can be found here. This has been a busy week with a rollout of some new website features here at my work, so I don’t have a big post for this week.  But I wanted to write something up, and since lately I’ve been renewing my C++ skills in a separate project, it seemed like a good opportunity to start a C++ Little Wonders series.  Most of my development work still tends to focus on C#, but it was great to get back into the saddle and renew my C++ knowledge.  Today I’m going to focus on a new feature in C++11 (formerly known as C++0x, which is a major move forward in the C++ language standard).  While this small keyword can seem so trivial, I feel it is a big step forward in improving readability in C++ programs. The auto keyword If you’ve worked on C++ for a long time, you probably have some passing familiarity with the old auto keyword as one of those rarely used C++ keywords that was almost never used because it was the default. That is, in the code below (before C++11): 1: int foo() 2: { 3: // automatic variables (allocated and deallocated on stack) 4: int x; 5: auto int y; 6:  7: // static variables (retain their value across calls) 8: static int z; 9:  10: return 0; 11: } The variable x is assumed to be auto because that is the default, thus it is unnecessary to specify it explicitly as in the declaration of y below that.  Basically, an auto variable is one that is allocated and de-allocated on the stack automatically.  Contrast this to static variables, that are allocated statically and exist across the lifetime of the program. Because auto was so rarely (if ever) used since it is the norm, they decided to remove it for this purpose and give it new meaning in C++11.  The new meaning of auto: implicit typing Now, if your compiler supports C++ 11 (or at least a good subset of C++11 or 0x) you can take advantage of type inference in C++.  For those of you from the C# world, this means that the auto keyword in C++ now behaves a lot like the var keyword in C#! For example, many of us have had to declare those massive type declarations for an iterator before.  Let’s say we have a std::map of std::string to int which will map names to ages: 1: std::map<std::string, int> myMap; And then let’s say we want to find the age of a given person: 1: // Egad that's a long type... 2: std::map<std::string, int>::const_iterator pos = myMap.find(targetName); Notice that big ugly type definition to declare variable pos?  Sure, we could shorten this by creating a typedef of our specific map type if we wanted, but now with the auto keyword there’s no need: 1: // much shorter! 2: auto pos = myMap.find(targetName); The auto now tells the compiler to determine what type pos should be based on what it’s being assigned to.  This is not dynamic typing, it still determines the type as if it were explicitly declared and once declared that type cannot be changed.  That is, this is invalid: 1: // x is type int 2: auto x = 42; 3:  4: // can't assign string to int 5: x = "Hello"; Once the compiler determines x is type int it is exactly as if we typed int x = 42; instead, so don’t' confuse it with dynamic typing, it’s still very type-safe. An interesting feature of the auto keyword is that you can modify the inferred type: 1: // declare method that returns int* 2: int* GetPointer(); 3:  4: // p1 is int*, auto inferred type is int 5: auto *p1 = GetPointer(); 6:  7: // ps is int*, auto inferred type is int* 8: auto p2 = GetPointer(); Notice in both of these cases, p1 and p2 are determined to be int* but in each case the inferred type was different.  because we declared p1 as auto *p1 and GetPointer() returns int*, it inferred the type int was needed to complete the declaration.  In the second case, however, we declared p2 as auto p2 which means the inferred type was int*.  Ultimately, this make p1 and p2 the same type, but which type is inferred makes a difference, if you are chaining multiple inferred declarations together.  In these cases, the inferred type of each must match the first: 1: // Type inferred is int 2: // p1 is int* 3: // p2 is int 4: // p3 is int& 5: auto *p1 = GetPointer(), p2 = 42, &p3 = p2; Note that this works because the inferred type was int, if the inferred type was int* instead: 1: // syntax error, p1 was inferred to be int* so p2 and p3 don't make sense 2: auto p1 = GetPointer(), p2 = 42, &p3 = p2; You could also use const or static to modify the inferred type: 1: // inferred type is an int, theAnswer is a const int 2: const auto theAnswer = 42; 3:  4: // inferred type is double, Pi is a static double 5: static auto Pi = 3.1415927; Thus in the examples above it inferred the types int and double respectively, which were then modified to const and static. Summary The auto keyword has gotten new life in C++11 to allow you to infer the type of a variable from it’s initialization.  This simple little keyword can be used to cut down large declarations for complex types into a much more readable form, where appropriate.   Technorati Tags: C++, C++11, Little Wonders, auto

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  • FireFox 6 Super Slow? Cache Settings Corruption

    - by Rick Strahl
    For those of you that follow me on Twitter, you've probably seen some of my tweets regarding major performance problems I've seen with the install of FireFox 6.0. FireFox 6.0 was released a couple of weeks ago and is treated as a 'force feed' update for FireFox 5.0. I'm not sure what the deal is with this braindead versioning that Mozilla is doing with major version releases coming out, what now every other month? Seriously that's retarded especially given the limited number of new features these releases bring, and the upgrade pain for plug-ins that the major version release causes. Anyway, after the FireFox updater bugged me long enough I finally gave in last week and updated to FireFox 6. Immediately after install I noticed terrible performance. Everything was running at a snail's pace with Web pages loading slowly and most content actually slowly 'painting' the page. A typical sign of content downloading slowly. However these are pages that should be mostly cached on my system and even repeated accesses ran just as slow. Just for a reality check I ran the same sites in Chrome (blazing fast) and IE (fast enough :-)) but FireFox - dog on a stick. Why so slow Boss? While complaining lots of people recommended to ditch FireFox - use Chrome, yada yada yada. Yeah, Chrome is fast and getting better but I have a number of plug-ins that I use in FF that I can't easily give up. So I suffered and started looking around more closely at what was happening. The first thing I noticed when accessing pages was that I continually saw accesses to the Google CDN downloading jQuery and jQuery UI. UI especially is pretty heavy in size and currently I'm in a location with a fairly slow IP connection where large files are a bit of an issue. However, seeing the CDN urls pop up repeatedly raised a flag with me. That stuff should be caching and it looked like each and every hit was reloading these scripts and various images over and over again. Fired up FireBug and sure enough I saw something like this on a repeated hit to my blog: Those two highlights are jquery and the main CSS file for the site and both are being loaded fully and taking a while to load. However, since this page had been loaded before, these items should be cached and show 304 requests instead of the full HTTP requests returning 200 result codes. In short it looked like FireFox was not caching ANY content at all and constantly reloading all page resources. No wonder things were running dog slow. Once I realized what the problem was I took a look in the about:config settings and lo and behold a bunch of the cache settings were set to not cache: In my case ALL the main cache flags were set to false for some reason that I can't figure out.  It appears that after the FireFox 6 update these flags somehow mysteriously changed and performance took a nose dive. Switching the .enable flags back to true and resetting all the cache settings tote default reverted performance back to the way it's supposed to be: reasonably fast and snappy as soon as content is cached and accessed again  from cache. I try not to muck with the about:config settings much (other than turning off the IPV6 option) but when there are problems access to these features can be really nice. However, I treat this as a last resort so it took me quite some time before I started looking through ALL the settings. This takes a while, not knowing what I was looking for exactly. If Web load performance is slow it's a good idea to check the cache settings. I have no idea what hosed these settings for me - I certainly didn't explicitly set them in about:config and while in FireFox's Options dialog I didn't see any option that would affect global caching like this, so this remains a mystery to me. Anyway, I hope that this is helpful to some, in case some of you end up running into a similar issue.© Rick Strahl, West Wind Technologies, 2005-2011Posted in FireFox   Tweet (function() { var po = document.createElement('script'); po.type = 'text/javascript'; po.async = true; po.src = 'https://apis.google.com/js/plusone.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(po, s); })();

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  • Understanding the static keyword

    - by user985482
    I have some experience in developing with Java, Javascript and PHP. I am reading Microsoft Visual C# 2010 Step by Step which I feel it is a very good book on introducing you to the C# language. I seem to be having problems in understanding the static keyword. From what I understand this far if a class is declared static all methods and variable have to be static. The main method always is a static method so in the class that the main method exists all variables and methods are declared static if you have to call them in the main method. Also I have noticed that in order to call a static method from another class you do not need to create an object of that you can use the class name. What are the advantages of declaring static variables and methods? When should I declare static variable and methods?

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