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• Hausman Test, Fixed/random effects in SAS?

  - by John

  Hey guys, I'm trying to do a fixed effecs OLS regression, a random effects OLS Regression and a Hausman test to back up my choice for one of those models. Alas, there does not seem to be a lot of information of what the code looks like when you want to do this. I found for the Hausman test that proc model data=one out=fiml2; endogenous y1 y2; y1 = py2 * y2 + px1 * x1 + interc; y2 = py1* y1 + pz1 * z1 + d2; fit y1 y2 / ols 2sls hausman; instruments x1 z1; run; you do something like this. However, I do not have the equations in the middle, which i assume to be the fixed and random effects models? On an other site I found that PROC TSCSREG automatically displays the Hausman test, unfortunately this does not work either. When I type PROC TSCSREG data = clean; data does not become blue meaning SAS does not recognize this as a type of data input? proc tscsreg data = clean; var nof capm_erm sigma cv fvyrgro meanest tvol bmratio size ab; run; I tried this but obviously doesn't work since it does not recognize the data input, I've been searching but I can't seem to find a proper example of how the code of an hausman test looks like. On the SAS site I neither find the code one has to use to perform a fixed/random effects model. My data has 1784 observations, 578 different firms (cross section?) and spans over a 2001-2006 period in months. Any help?

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• Ray Generation Inconsistency

  - by Myx

  I have written code that generates a ray from the "eye" of the camera to the viewing plane some distance away from the camera's eye: R3Ray ConstructRayThroughPixel(...) { R3Point p; double increments_x = (lr.X() - ul.X())/(double)width; double increments_y = (ul.Y() - lr.Y())/(double)height; p.SetX( ul.X() + ((double)i_pos+0.5)*increments_x ); p.SetY( lr.Y() + ((double)j_pos+0.5)*increments_y ); p.SetZ( lr.Z() ); R3Vector v = p-camera_pos; R3Ray new_ray(camera_pos,v); return new_ray; } ul is the upper left corner of the viewing plane and lr is the lower left corner of the viewing plane. They are defined as follows: R3Point org = scene->camera.eye + scene->camera.towards * radius; R3Vector dx = scene->camera.right * radius * tan(scene->camera.xfov); R3Vector dy = scene->camera.up * radius * tan(scene->camera.yfov); R3Point lr = org + dx - dy; R3Point ul = org - dx + dy; Here, org is the center of the viewing plane with radius being the distance between the viewing plane and the camera eye, dx and dy are the displacements in the x and y directions from the center of the viewing plane. The ConstructRayThroughPixel(...) function works perfectly for a camera whose eye is at (0,0,0). However, when the camera is at some different position, not all needed rays are produced for the image. Any suggestions what could be going wrong? Maybe something wrong with my equations? Thanks for the help.

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• Code bacteria: evolving mathematical behavior

  - by Stefano Borini

  It would not be my intention to put a link on my blog, but I don't have any other method to clarify what I really mean. The article is quite long, and it's in three parts (1,2,3), but if you are curious, it's worth the reading. A long time ago (5 years, at least) I programmed a python program which generated "mathematical bacteria". These bacteria are python objects with a simple opcode-based genetic code. You can feed them with a number and they return a number, according to the execution of their code. I generate their genetic codes at random, and apply an environmental selection to those objects producing a result similar to a predefined expected value. Then I let them duplicate, introduce mutations, and evolve them. The result is quite interesting, as their genetic code basically learns how to solve simple equations, even for values different for the training dataset. Now, this thing is just a toy. I had time to waste and I wanted to satisfy my curiosity. however, I assume that something, in terms of research, has been made... I am reinventing the wheel here, I hope. Are you aware of more serious attempts at creating in-silico bacteria like the one I programmed? Please note that this is not really "genetic algorithms". Genetic algorithms is when you use evolution/selection to improve a vector of parameters against a given scoring function. This is kind of different. I optimize the code, not the parameters, against a given scoring function.

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• How to automatically read in calculated values with PHPExcel?

  - by Edward Tanguay

  I have the following Excel file: I read it in by looping over every cell and getting the value with getCell(...)->getValue(): $highestColumnAsLetters = $this->objPHPExcel->setActiveSheetIndex(0)->getHighestColumn(); //e.g. 'AK' $highestRowNumber = $this->objPHPExcel->setActiveSheetIndex(0)->getHighestRow(); $highestColumnAsLetters++; for ($row = 1; $row < $highestRowNumber + 1; $row++) { $dataset = array(); for ($columnAsLetters = 'A'; $columnAsLetters != $highestColumnAsLetters; $columnAsLetters++) { $dataset[] = $this->objPHPExcel->setActiveSheetIndex(0)->getCell($columnAsLetters.$row)->getValue(); if ($row == 1) { $this->column_names[] = $columnAsLetters; } } $this->datasets[] = $dataset; } However, although it reads in the data fine, it reads in the calculations literally: I understand from discussions like this one that I can use getCalculatedValue() for calculated cells. The problem is that in the Excel sheets I am importing, I do not know beforehand which cells are calculated and which are not. Is there a way for me to read in the value of a cell in a way that automatically gets the value if it has a simple value and gets the result of the calculation if it is a calculation? Answer: It turns out that getCalculatedValue() works for all cells, makes me wonder why this isn't the default for getValue() since I would think one would usually want the value of the calculations instead of the equations themselves, in any case this works: ...->getCell($columnAsLetters.$row)->getCalculatedValue();

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• Does SetFileBandwidthReservation affect memory-mapped file performance?

  - by Ghostrider

  Does this function affect Memory-mapped file performance? Here's the problem I need to solve: I have two applications competing for disk access: "reader" and "updater". Whole system runs on Windows Server 2008 R2 x64 "Updater" constantly accesses disk in a linear manner, updating data. They system is set up in such a way that updater always has infinite data to update. Consider that it is constantly approximating a solution of a huge set of equations that takes up entire 2TB disk drive. Updater uses ReadFile and WriteFile to process data in a linear fashion. "Reader" is occasionally invoked by user to get some pieces of data. Usually user would read several 4kb blocks from the drive and stop. Occasionally user needs to read up to 100mb sequentially. In exceptional cases up to several gigabytes. Reader maps files to memory to get data it needs. What I would like to achieve is for "reader" to have absolute priority so that "updater" would completely stop if needed so that "reader" could get the data user needs ASAP. Is this problem solvable by using SetPriorityClass and SetFileBandwidthReservation calls? I would really hate to put synchronization login in "reader" and "updater" and rather have the OS take care of priorities.

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• Linear regression confidence intervals in SQL

  - by Matt Howells

  I'm using some fairly straight-forward SQL code to calculate the coefficients of regression (intercept and slope) of some (x,y) data points, using least-squares. This gives me a nice best-fit line through the data. However we would like to be able to see the 95% and 5% confidence intervals for the line of best-fit (the curves below). What these mean is that the true line has 95% probability of being below the upper curve and 95% probability of being above the lower curve. How can I calculate these curves? I have already read wikipedia etc. and done some googling but I haven't found understandable mathematical equations to be able to calculate this. Edit: here is the essence of what I have right now. --sample data create table #lr (x real not null, y real not null) insert into #lr values (0,1) insert into #lr values (4,9) insert into #lr values (2,5) insert into #lr values (3,7) declare @slope real declare @intercept real --calculate slope and intercept select @slope = ((count(*) * sum(x*y)) - (sum(x)*sum(y)))/ ((count(*) * sum(Power(x,2)))-Power(Sum(x),2)), @intercept = avg(y) - ((count(*) * sum(x*y)) - (sum(x)*sum(y)))/ ((count(*) * sum(Power(x,2)))-Power(Sum(x),2)) * avg(x) from #lr Thank you in advance.

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• Accelerometer gravity components

  - by Dvd

  Hi, I know this question is definitely solved somewhere many times already, please enlighten me if you know of their existence, thanks. Quick rundown: I want to compute from a 3 axis accelerometer the gravity component on each of these 3 axes. I have used 2 axes free body diagrams to work out the accelerometer's gravity component in the world X-Z, Y-Z and X-Y axes. But the solution seems slightly off, it's acceptable for extreme cases when only 1 accelerometer axis is exposed to gravity, but for a pitch and roll of both 45 degrees, the combined total magnitude is greater than gravity (obtained by Xa^2+Ya^2+Za^2=g^2; Xa, Ya and Za are accelerometer readings in its X, Y and Z axis). More detail: The device is a Nexus One, and have a magnetic field sensor for azimuth, pitch and roll in addition to the 3-axis accelerometer. In the world's axis (with Z in the same direction as gravity, and either X or Y points to the north pole, don't think this matters much?), I assumed my device has a pitch (P) on the Y-Z axis, and a roll (R) on the X-Z axis. With that I used simple trig to get: Sin(R)=Ax/Gxz Cos(R)=Az/Gxz Tan(R)=Ax/Az There is another set for pitch, P. Now I defined gravity to have 3 components in the world's axis, a Gxz that is measurable only in the X-Z axis, a Gyz for Y-Z, and a Gxy for X-Y axis. Gxz^2+Gyz^2+Gxy^2=2*G^2 the 2G is because gravity is effectively included twice in this definition. Oh and the X-Y axis produce something more exotic... I'll explain if required later. From these equations I obtained a formula for Az, and removed the tan operations because I don't know how to handle tan90 calculations (it's infinity?). So my question is, anyone know whether I did this right/wrong or able to point me to the right direction? Thanks! Dvd

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• How to handle alpha in a manual "Overlay" blend operation?

  - by quixoto

  I'm playing with some manual (walk-the-pixels) image processing, and I'm recreating the standard "overlay" blend. I'm looking at the "Photoshop math" macros here: http://www.nathanm.com/photoshop-blending-math/ (See also here for more readable version of Overlay) Both source images are in fairly standard RGBA (8 bits each) format, as is the destination. When both images are fully opaque (alpha is 1.0), the result is blended correctly as expected: But if my "blend" layer (the top image) has transparency in it, I'm a little flummoxed as to how to factor that alpha into the blending equation correctly. I expect it to work such that transparent pixels in the blend layer have no effect on the result, opaque pixels in the blend layer do the overlay blend as normal, and semitransparent blend layer pixels have some scaled effect on the result. Can someone explain to me the blend equations or the concept behind doing this? Bonus points if you can help me do it such that the resulting image has correctly premultiplied alpha (which only comes into play for pixels that are not opaque in both layers, I think.) Thanks! // factor in blendLayerA, (1-blendLayerA) somehow? resultR = ChannelBlend_Overlay(baseLayerR, blendLayerR); resultG = ChannelBlend_Overlay(baseLayerG, blendLayerG); resultB = ChannelBlend_Overlay(baseLayerB, blendLayerB); resultA = 1.0; // also, what should this be??

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• How to Implement Overlay blend method using opengles 1.1

  - by Cylon

  Blow is the algorithm of overlay. and i want using it on iphone, but iphone 3g only support opengles 1.1, can not using glsl. can i using blend function or texture combine to implement it. thank you /////////Reference from OpenGL Shading® Language Third Edition /////////// 19.6.12 Overlay OVERLAY first computes the luminance of the base value. If the luminance value is less than 0.5, the blend and base values are multiplied together. If the luminance value is greater than 0.5, a screen operation is performed. The effect is that the base value is mixed with the blend value, rather than being replaced. This allows patterns and colors to overlay the base image, but shadows and highlights in the base image are preserved. A discontinuity occurs where luminance = 0.5. To provide a smooth transition, we actually do a linear blend of the two equations for luminance in the range [0.45,0.55]. float luminance = dot(base, lumCoeff); if (luminance < 0.45) result = 2.0 * blend * base; else if (luminance 0.55) result = white - 2.0 * (white - blend) * (white - base); else { vec4 result1 = 2.0 * blend * base; vec4 result2 = white - 2.0 * (white - blend) * (white - base); result = mix(result1, result2, (luminance - 0.45) * 10.0); }

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• Simple encryption - Sum of Hashes in C

  - by Dogbert

  I am attempting to demonstrate a simple proof of concept with respect to a vulnerability in a piece of code in a game written in C. Let's say that we want to validate a character login. The login is handled by the user choosing n items, (let's just assume n=5 for now) from a graphical menu. The items are all medieval themed: eg: _______________________________ | | | | | Bow | Sword | Staff | |-----------|-----------|-------| | Shield | Potion | Gold | |___________|___________|_______| The user must click on each item, then choose a number for each item. The validation algorithm then does the following: Determines which items were selected Drops each string to lowercase (ie: Bow becomes bow, etc) Calculates a simple string hash for each string (ie: `bow = b=2, o=15, w=23, sum = (2+15+23=40) Multiplies the hash by the value the user selected for the corresponding item; This new value is called the key Sums together the keys for each of the selected items; this is the final validation hash IMPORTANT: The validator will accept this hash, along with non-zero multiples of it (ie: if the final hash equals 1111, then 2222, 3333, 8888, etc are also valid). So, for example, let's say I select: Bow (1) Sword (2) Staff (10) Shield (1) Potion (6) The algorithm drops each of these strings to lowercase, calculates their string hashes, multiplies that hash by the number selected for each string, then sums these keys together. eg: Final_Validation_Hash = 1*HASH(Bow) + 2*HASH(Sword) + 10*HASH(Staff) + 1*HASH(Shield) + 6*HASH(Potion) By application of Euler's Method, I plan to demonstrate that these hashes are not unique, and want to devise a simple application to prove it. in my case, for 5 items, I would essentially be trying to calculate: (B)(y) = (A_1)(x_1) + (A_2)(x_2) + (A_3)(x_3) + (A_4)(x_4) + (A_5)(x_5) Where: B is arbitrary A_j are the selected coefficients/values for each string/category x_j are the hash values for each string/category y is the final validation hash (eg: 1111 above) B,y,A_j,x_j are all discrete-valued, positive, and non-zero (ie: natural numbers) Can someone either assist me in solving this problem or point me to a similar example (ie: code, worked out equations, etc)? I just need to solve the final step (ie: (B)(Y) = ...). Thank you all in advance.

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• Assign sage variable values into R objects via sagetex and Sweave

  - by sheed03

  I am writing a short Sweave document that outputs into a Beamer presentation, in which I am using the sagetex package to solve an equation for two parameters in the beta binomial distribution, and I need to assign the parameter values into the R session so I can do additional processing on those values. The following code excerpt shows how I am interacting with sage: <<echo=false,results=hide>>= mean.raw <- c(5, 3.5, 2) theta <- 0.5 var.raw <- mean.raw + ((mean.raw^2)/theta) @ \begin{frame}[fragile] \frametitle{Test of Sage 2} \begin{sagesilent} var('a1, b1, a2, b2, a3, b3') eqn1 = [1000*a1/(a1+b1)==\Sexpr{mean.raw[1]}, ((1000*a1*b1)*(1000+a1+b1))/((a1+b1)^2*(a1+b1+1))==\Sexpr{var.raw[1]}] eqn2 = [1000*a2/(a2+b2)==\Sexpr{mean.raw[2]}, ((1000*a2*b2)*(1000+a2+b2))/((a2+b2)^2*(a2+b2+1))==\Sexpr{var.raw[2]}] eqn3 = [1000*a3/(a3+b3)==\Sexpr{mean.raw[3]}, ((1000*a3*b3)*(1000+a3+b3))/((a3+b3)^2*(a3+b3+1))==\Sexpr{var.raw[3]}] s1 = solve(eqn1, a1,b1) s2 = solve(eqn2, a2,b2) s3 = solve(eqn3, a3,b3) \end{sagesilent} Solutions of Beta Binomial Parameters: \begin{itemize} \item $\sage{s1[0]}$ \item $\sage{s2[0]}$ \item $\sage{s3[0]}$ \end{itemize} \end{frame} Everything compiles just fine, and in that slide I am able to see the solutions to the three equations respective parameters in that itemized list (for example the first item in the itemized list from that beamer slide is outputted as [a1=(328/667), b1=(65272/667)] (I am not able to post an image of the beamer slide but I hope you get the idea). I would like to save the parameter values a1,b1,a2,b2,a3,b3 into R objects so that I can use them in simulations. I cannot find any documentation in the sagetex package on how to save output from sage commands into variables for use with other programs (in this case R). Any suggestions on how to get these values into R?

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• Collision of dot and line in 2D space

  - by Anderiel

  So i'm trying to make my first game on android. The thing is i have a small moving ball and i want it to bounce from a line that i drew. For that i need to find if the x,y of the ball are also coordinates of one dot from the line. I tried to implement these equations about lines x=a1 + t*u1 y=a2 + t*u2 = (x-a1)/u1=(y-a2)/u2 (t=t which has to be if the point is on the line) where x and y are the coordinates im testing, dot[a1,a2] is a dot that is on the line and u(u1,u2) is the vector of the line. heres the code: public boolean Collided() { float u1 =Math.abs(Math.round(begin_X)-Math.round(end_X)); float u2 =Math.abs(Math.round(begin_Y)-Math.round(end_Y)); float t_x =Math.round((elect_X - begin_X)/u1); float t_y =Math.round((elect_Y - begin_Y)/u2); if(t_x==t_y) { return true; } else { return false; } } points [begin_X,end_X] and [begin_Y,end_Y] are the two points from the line and [elect_X,elect_Y] are the coordinates of the ball theoreticaly it should work, but in the reality the ball most of the time just goes straigth through the line or bounces somewhere else where it shouldnt

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• How do I become better in math, after being a programmer for several years.

  - by loxs

  I've had quite a weird career till now. First I graduated from a medical school. Then I went into marketing (pharmaceuticals). And then umm, after some time, I decided to go for my (till then) hobby and became a "professional" programmer. I've been quite successful at this ever since. I have quite some languages "under my belt". I earn not bad and I have been involved in the opensource community quite heavily. The thing is that I suck at math :). Well, not totally of course, as I get my work done. But I don't know how much I suck. And I don't know how to find out. Math has never really been of any priority during my middle/high school years. I only picked as little as I could afford, because I was always getting ready to go for Medicine. Of course I know the basics of algebra. Things like "normal" and square equations. Also the basics of geometry. But well, there are things that I have missed. And lately I am being fascinated by things like probability theory, infinity, chaos/order etc. But every time I try to learn something about these topics, I hit a wall of terminology, special symbols, and some special kind of thinking, that is quite like mine (a programmer), but also a lot different (and appears weird to me). So, what kinds of books would you recommend me? It's very hard to find something suitable. All that I find are either too easy (and boring) or totally impenetrable.

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• Generic applet style system for publishing mathematics demonstrations?

  - by Alex

  Anyone who's tried to study mathematics using online resources will have come across these Java applets that demonstrate a particular mathematical idea. Examples: http://www.math.ucla.edu/~tao/java/Mobius.html http://www.mathcs.org/java/programs/FFT/index.html I love the idea of this interactive approach because I believe it is very helpful in conveying mathematical principles. I'd like to create a system for visually designing and publishing these 'mathlets' such that they can be created by teachers with little programming experience. So in order to create this app, i'll need a GUI and a 'math engine'. I'll probably be working with .NET because thats what I know best and i'd like to start experimenting with F#. Silverlight appeals to me as a presentation framework for this project (im not worried about interoperability right now). So my questions are: does anything like this exist already in full form? are there any GUI frameworks for displaying mathematical objects such as graphs & equations? are there decent open source libraries that exposes a mathematical framework (Math.NET looks good, just wondering if there is anything else out there) is there any existing work on taking mathematical models/demos built with maple/matlab/octave/mathematica etc and publishing them to the web?

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• Solving problems with near infinite potential solutions

  - by Zonda333

  Today I read the following problem: Use the digits 2, 0, 1, 1 and the operations +, -, x, ÷, sqrt, ^ , !, (), combinations, and permutations to write equations for the counting numbers 1 through 100. All four digits must be used in each expression. Only the digits 2, 0, 1, 1 may be used, and each must be used exactly once. Decimals may be used, as in .1, .02, etc. Digits may be combined; numbers such as 20 or 101 may be used. Example: 60 = 10*(2+1)!, 54 = ¹¹C2 - 0! Though I was able to quickly find around 50 solutions quite easily in my head, I thought programming it would be a far superior solution. However, I then realized I had no clue how to go about solving a problem like this. I am not asking for complete code for me to copy and paste, but for ideas about how I would solve this problems, and others like it that have nearly infinite potential solutions. As I will be writing it in python, where I have the most experience, I would prefer if the answers were more python based, but general ideas are great too.

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• ReplaceAll not working as expected

  - by Tim Kemp

  Still early days with Mathematica so please forgive what is probably a very obvious question. I am trying to generate some parametric plots. I have: ParametricPlot[{ (a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, {t, 0, 2 \[Pi]}, PlotRange -> All] /. {a -> 2, b -> 1, h -> 1} No joy: the replacement rules are not applied and a, b and h remain undefined. If I instead do: Hold@ParametricPlot[{ (a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, {t, 0, 2 \[Pi]}, PlotRange -> All] /. {a -> 2, b -> 1, h -> 1} it looks like the rules ARE working, as confirmed by the output: Hold[ParametricPlot[{(2 + 1) Cos[t] - 1 Cos[(2 + 1) t], (2 + 1) Sin[t] - 1 Sin[(2 + 1) t]}, {t, 0, 2 \[Pi]}, PlotRange -> All]] Which is what I'd expect. Take the Hold off, though, and the ParametricPlot doesn't work. There's nothing wrong with the equations or the ParametricPlot itself, though, because I tried setting values for a, b and h in a separate expression (a=2; b=1; h=1) and I get my pretty double cardoid out as expected. So, what am I doing wrong with ReplaceAll and why are the transformation rules not working? This is another fundamentally important aspect of MMA that my OOP-ruined brain isn't understanding. I tried reading up on ReplaceAll and ParametricPlot and the closest clue I found was that "ParametricPlot has attribute HoldAll and evaluates f only after assigning specific numerical values to variables" which didn't help much or I wouldn't be here. Thanks.

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• changing the intensity of lighten/darken on bitmaps using PorterDuffXfermode in the Android Paint class

  - by user1116836

  Ok my orignal question has changed. How do i change the intensity of how something like this is effected? DayToNight.setXfermode(new PorterDuffXfermode(Mode.DST_IN)); in my dream world it would have worked like this DayToNight.setXfermode(new PorterDuffXfermode(Mode.DST_IN(10))); the 10 being a level of intensity. An example would be if I had a flickering candle, when the candle burns bright I want the bitmaps I am drawing to the screen to retain their origanol color and brightness, when it flickers I want the bitmaps to be almost blacked out, and I want to darken the Bitmaps as the light dims. I have equations, timers and all that figured out, just not how to actually apply it to change the color/brightness. Maybe burning the images is what im looking for? I just want to change the lightness lol. I feel like using paint.setShader might be a solution, but the information in this area is pretty limited from what i have been able to find. Any help would be appreciated. edit: to be crystal clear, i am looking for a way to lighten/darken bitmaps as I draw them to the canvas

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• printSoln module problem

  - by dingo_d

  Hi I found in book:Numerical Methods in engineering with Python the module run_kut5, but for that module I need module printSoln, all provided in the book. Now I cp the code, made necessary line adjustments and so. The code looks like: # -*- coding: cp1250 -*- ## module printSoln ''' printSoln(X,Y,freq). Prints X and Y returned from the differential equation solvers using printput frequency ’freq’. freq = n prints every nth step. freq = 0 prints initial and final values only. ''' def printSoln(X,Y,freq): def printHead(n): print "\n x ", for i in range (n): print " y[",i,"] ", print def printLine(x,y,n): print "%13.4e"% x,f for i in range (n): print "%13.4e"% y[i], print m = len(Y) try: n = len(Y[0]) except TypeError: n = 1 if freq == 0: freq = m printHead(n) for i in range(0,m,freq): printLine(X[i],Y[i],n) if i != m - 1: printLine(X[m - 1],Y[m - 1],n) Now, when I run the program it says: line 24, in <module> m = len(Y) NameError: name 'Y' is not defined But I cp'd from the book :\ So now when I call the run_kut module I get the same error, no Y defined in printSoln... I'm trying to figure this out but I suck :( Help, please...

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• 6 Interesting Facts About NASA’s Mars Rover ‘Curiosity’

  - by Gopinath

  Humans quest for exploring the surrounding planets to see whether we can live there or not is taking new shape today. NASA’s Mars probing robot, Curiosity, blasted off today on its 9 months journey to reach Mars and explore it for the possibilities of life there. Scientist says that Curiosity is one most advanced rover ever launched to probe life on other planets. Here is the launch video and some analysis by a news reporter Lets look at the 6 interesting facts about the mission 1. It’s as big as a car Curiosity is the biggest ever rover ever launched by NASA to probe life on outer planets. It’s as big as a car and almost double the size of its predecessor rover Spirit. The length of Curiosity is around 9 feet 10 inches(3 meters), width is 9 feet 1 inch (2.8 meters) and height is 7 feet (2.1 meters). 2. Powered by Plutonium – Lasts 24×7 for 23 months The earlier missions of NASA to explore Mars are powered by Solar power and that hindered capabilities of the rovers to move around when the Sun is hiding. Due to dependency of Sun the earlier rovers were not able to traverse the places where there is no Sun light. Curiosity on the other hand is equipped with a radioisotope power system that generates electricity from the heat emitted by plutonium’s radioactive decay. The plutonium weighs around 10 pounds and can generate power required for operating the rover close to 23 weeks. The best part of the new power system is, Curiosity can roam around in darkness, light and all year around. 3. Rocket powered backpack for a science fiction style landing The Curiosity is so heavy that NASA could not use parachute and balloons to air-drop the rover on the surface of Mars like it’s previous missions. They are trying out a new science fiction style air-dropping mechanism that is similar to sky crane heavy-lift helicopter. The landing of the rover begins first with entry into the Mars atmosphere protected by a heat shield. At about 6 miles to the surface, the heat shield is jettisoned and a parachute is deployed to glide the rover smoothly. When the rover touches 3 miles above the surface, the parachute is jettisoned and the eight motors rocket backpack is used for a smooth and impact free landing as shown in the image. Here is an animation created by NASA on the landing sequence. If you are interested in getting more detailed information about the landing process check this landing sequence picture available on NASA website 4. Equipped with Star Wars style laser gun Hollywood movie directors and novelist always imagined aliens coming to earth with spaceships full of laser guns and blasting the objects which comes on their way. With Curiosity the equations are going to change. It has a powerful laser gun equipped in one of it’s arms to beam laser on rocks to vaporize them. This is not part of any assault mission Curiosity is expected to carry out, the laser gun is will be used to carry out experiments to detect life and understand nature. 5. Most sophisticated laboratory powered by 10 instruments Around 10 state of art instruments are part of Curiosity rover and the these 10 instruments form a most advanced rover based lab ever built by NASA. There are instruments to cut through rocks to examine them and other instruments will search for organic compounds. Mounted cameras can study targets from a distance, arm mounted instruments can study the targets they touch. Microscopic lens attached to the arm can see and magnify tiny objects as tiny as 12.5 micro meters. 6. Rover Carrying 1.24 million names etched on silicon Early June 2009 NASA launched a campaign called “Send Your Name to Mars” and around 1.24 million people registered their names through NASA’s website. All those 1.24 million names are etched on Silicon chips mounted onto Curiosity’s deck. If you had registered your name in the campaign may be your name is going to reach Mars soon. Curiosity On Web If you wish to follow the mission here are few links to help you NASA’s Curiosity Web Page Follow Curiosity on Facebook Follow @MarsCuriosity on Twitter Artistic Gallery Image of Mars Rover Curiosity A printable sheet of Curiosity Mission [pdf] Images credit: NASA This article titled,6 Interesting Facts About NASA’s Mars Rover ‘Curiosity’, was originally published at Tech Dreams. Grab our rss feed or fan us on Facebook to get updates from us.

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• SQL SERVER – Beginning of SQL Server Architecture – Terminology – Guest Post

  - by pinaldave

  SQL Server Architecture is a very deep subject. Covering it in a single post is an almost impossible task. However, this subject is very popular topic among beginners and advanced users.  I have requested my friend Anil Kumar who is expert in SQL Domain to help me write  a simple post about Beginning SQL Server Architecture. As stated earlier this subject is very deep subject and in this first article series he has covered basic terminologies. In future article he will explore the subject further down. Anil Kumar Yadav is Trainer, SQL Domain, Koenig Solutions. Koenig is a premier IT training firm that provides several IT certifications, such as Oracle 11g, Server+, RHCA, SQL Server Training, Prince2 Foundation etc. In this Article we will discuss about MS SQL Server architecture. The major components of SQL Server are: Relational Engine Storage Engine SQL OS Now we will discuss and understand each one of them. 1) Relational Engine: Also called as the query processor, Relational Engine includes the components of SQL Server that determine what your query exactly needs to do and the best way to do it. It manages the execution of queries as it requests data from the storage engine and processes the results returned. Different Tasks of Relational Engine: Query Processing Memory Management Thread and Task Management Buffer Management Distributed Query Processing 2) Storage Engine: Storage Engine is responsible for storage and retrieval of the data on to the storage system (Disk, SAN etc.). to understand more, let’s focus on the following diagram. When we talk about any database in SQL server, there are 2 types of files that are created at the disk level – Data file and Log file. Data file physically stores the data in data pages. Log files that are also known as write ahead logs, are used for storing transactions performed on the database. Let’s understand data file and log file in more details: Data File: Data File stores data in the form of Data Page (8KB) and these data pages are logically organized in extents. Extents: Extents are logical units in the database. They are a combination of 8 data pages i.e. 64 KB forms an extent. Extents can be of two types, Mixed and Uniform. Mixed extents hold different types of pages like index, System, Object data etc. On the other hand, Uniform extents are dedicated to only one type. Pages: As we should know what type of data pages can be stored in SQL Server, below mentioned are some of them: Data Page: It holds the data entered by the user but not the data which is of type text, ntext, nvarchar(max), varchar(max), varbinary(max), image and xml data. Index: It stores the index entries. Text/Image: It stores LOB ( Large Object data) like text, ntext, varchar(max), nvarchar(max),  varbinary(max), image and xml data. GAM & SGAM (Global Allocation Map & Shared Global Allocation Map): They are used for saving information related to the allocation of extents. PFS (Page Free Space): Information related to page allocation and unused space available on pages. IAM (Index Allocation Map): Information pertaining to extents that are used by a table or index per allocation unit. BCM (Bulk Changed Map): Keeps information about the extents changed in a Bulk Operation. DCM (Differential Change Map): This is the information of extents that have modified since the last BACKUP DATABASE statement as per allocation unit. Log File: It also known as write ahead log. It stores modification to the database (DML and DDL). Sufficient information is logged to be able to: Roll back transactions if requested Recover the database in case of failure Write Ahead Logging is used to create log entries Transaction logs are written in chronological order in a circular way Truncation policy for logs is based on the recovery model SQL OS: This lies between the host machine (Windows OS) and SQL Server. All the activities performed on database engine are taken care of by SQL OS. It is a highly configurable operating system with powerful API (application programming interface), enabling automatic locality and advanced parallelism. SQL OS provides various operating system services, such as memory management deals with buffer pool, log buffer and deadlock detection using the blocking and locking structure. Other services include exception handling, hosting for external components like Common Language Runtime, CLR etc. I guess this brief article gives you an idea about the various terminologies used related to SQL Server Architecture. In future articles we will explore them further. Guest Author  The author of the article is Anil Kumar Yadav is Trainer, SQL Domain, Koenig Solutions. Koenig is a premier IT training firm that provides several IT certifications, such as Oracle 11g, Server+, RHCA, SQL Server Training, Prince2 Foundation etc. Reference: Pinal Dave (http://blog.sqlauthority.com) Filed under: PostADay, SQL, SQL Authority, SQL Query, SQL Security, SQL Server, SQL Tips and Tricks, SQL Training, T SQL, Technology

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• SQL SERVER – SSMS: Backup and Restore Events Report

  - by Pinal Dave

  A DBA wears multiple hats and in fact does more than what an eye can see. One of the core task of a DBA is to take backups. This looks so trivial that most developers shrug this off as the only activity a DBA might be doing. I have huge respect for DBA’s all around the world because even if they seem cool with all the scripting, automation, maintenance works round the clock to keep the business working almost 365 days 24×7, their worth is knowing that one day when the systems / HDD crashes and you have an important delivery to make. So these backup tasks / maintenance jobs that have been done come handy and are no more trivial as they might seem to be as considered by many. So the important question like: “When was the last backup taken?”, “How much time did the last backup take?”, “What type of backup was taken last?” etc are tricky questions and this report lands answers to the same in a jiffy. So the SSMS report, we are talking can be used to find backups and restore operation done for the selected database. Whenever we perform any backup or restore operation, the information is stored in the msdb database. This report can utilize that information and provide information about the size, time taken and also the file location for those operations. Here is how this report can be launched.   Once we launch this report, we can see 4 major sections shown as listed below. Average Time Taken For Backup Operations Successful Backup Operations Backup Operation Errors Successful Restore Operations Let us look at each section next. Average Time Taken For Backup Operations Information shown in “Average Time Taken For Backup Operations” section is taken from a backupset table in the msdb database. Here is the query and the expanded version of that particular section USE msdb; SELECT (ROW_NUMBER() OVER (ORDER BY t1.TYPE))%2 AS l1 ,       1 AS l2 ,       1 AS l3 ,       t1.TYPE AS [type] ,       (AVG(DATEDIFF(ss,backup_start_date, backup_finish_date)))/60.0 AS AverageBackupDuration FROM backupset t1 INNER JOIN sys.databases t3 ON ( t1.database_name = t3.name) WHERE t3.name = N'AdventureWorks2014' GROUP BY t1.TYPE ORDER BY t1.TYPE On my small database the time taken for differential backup was less than a minute, hence the value of zero is displayed. This is an important piece of backup operation which might help you in planning maintenance windows. Successful Backup Operations Here is the expanded version of this section.   This information is derived from various backup tracking tables from msdb database.  Here is the simplified version of the query which can be used separately as well. SELECT * FROM sys.databases t1 INNER JOIN backupset t3 ON (t3.database_name = t1.name) LEFT OUTER JOIN backupmediaset t5 ON ( t3.media_set_id = t5.media_set_id) LEFT OUTER JOIN backupmediafamily t6 ON ( t6.media_set_id = t5.media_set_id) WHERE (t1.name = N'AdventureWorks2014') ORDER BY backup_start_date DESC,t3.backup_set_id,t6.physical_device_name; The report does some calculations to show the data in a more readable format. For example, the backup size is shown in KB, MB or GB. I have expanded first row by clicking on (+) on “Device type” column. That has shown me the path of the physical backup file. Personally looking at this section, the Backup Size, Device Type and Backup Name are critical and are worth a note. As mentioned in the previous section, this section also has the Duration embedded inside it. Backup Operation Errors This section of the report gets data from default trace. You might wonder how. One of the event which is tracked by default trace is “ErrorLog”. This means that whatever message is written to errorlog gets written to default trace file as well. Interestingly, whenever there is a backup failure, an error message is written to ERRORLOG and hence default trace. This section takes advantage of that and shows the information. We can read below message under this section, which confirms above logic. No backup operations errors occurred for (AdventureWorks2014) database in the recent past or default trace is not enabled. Successful Restore Operations This section may not be very useful in production server (do you perform a restore of database?) but might be useful in the development and log shipping secondary environment, where we might be interested to see restore operations for a particular database. Here is the expanded version of the section. To fill this section of the report, I have restored the same backups which were taken to populate earlier sections. Here is the simplified version of the query used to populate this output. USE msdb; SELECT * FROM restorehistory t1 LEFT OUTER JOIN restorefile t2 ON ( t1.restore_history_id = t2.restore_history_id) LEFT OUTER JOIN backupset t3 ON ( t1.backup_set_id = t3.backup_set_id) WHERE t1.destination_database_name = N'AdventureWorks2014' ORDER BY restore_date DESC,  t1.restore_history_id,t2.destination_phys_name Have you ever looked at the backup strategy of your key databases? Are they in sync and do we have scope for improvements? Then this is the report to analyze after a week or month of maintenance plans running in your database. Do chime in with what are the strategies you are using in your environments. Reference: Pinal Dave (http://blog.sqlauthority.com)Filed under: PostADay, SQL, SQL Authority, SQL Backup and Restore, SQL Query, SQL Server, SQL Server Management Studio, SQL Tips and Tricks, T SQL Tagged: SQL Reports

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• SQL SERVER – Recover the Accidentally Renamed Table

  - by pinaldave

  I have no answer to following question. I saw a desperate email marked as urgent delivered in my mailbox. “I accidentally renamed table in my SSMS. I was scrolling very fast and I made mistakes. It was either because I double clicked or clicked on F2 (shortcut key for renaming). However, I have made the mistake and now I have no idea how to fix this. I am in big trouble. Help me get my original tablename.” I have seen many similar scenarios in my life and they give me a very good opportunity to preach wisdom but when the house is burning, we cannot talk about how we should have conserved the water earlier. The goal at that point is to put off the fire as fast as we can. I decided to answer this email with my best knowledge. If you have renamed the table, I think you pretty much is out of luck. Here are few things which you can do which can give you idea about what your tablename can be if you are lucky. Method 1: (Not Recommended but try your luck) Check your naming convention of your system. I have often seen that many organizations name their index as IX_TableName_Colms or name their keys as FK_TableName1_TableName2_Cols. If your organization is following the same you can get the name from your table, you may refer your keys. Again, note that this is quite possible that your tablename was already renamed and your keys were not updated. This can easily lead you to select incorrect name. I think follow this if you are confident or move to the next method. Method 2: (Not Recommended but try your luck) This method is also based on your orgs naming convention. If you use the name of the table in any columnname (some organizations use tablename in their incremental identity column name), you can get that name from there. Method 3: (Not Recommended but try your luck) If you know where your table was used in your stored procedures, you can script your stored procedure and find the name of the table back. Method 4: (Try your luck) All the best organizations first create a data model of the schema and there is good chance that this table is used there, you should take your chances and refer original document. If your organization is good at managing docs or source code, you will get the name of the table back for sure. Method 5: (It WORKS but try on a development server) There is no sure way to get you the name of the table which you accidentally renamed however, there is one way which will work for sure. You need to take your latest full backup and restore it on your development server (remember not on production or where you have renamed this column). Now restore latest differential file of the full backup. Now restore all the log files one by one making sure that you are restoring before the point of time of you renamed the tablename. Now go to explore and this will give you the name of the table which you have renamed. If you are confident that the same table existed with the same name when the last full backup was made, you do not have to go to all the steps. You can just get the name of the table directly from last backup’s restore. Read the article about Backup Timeline. Wisdom: How can I miss to preach wisdom when I get the opportunity to do so? Here are a few points to remember. Use a different account to explore production environment. Do not use the same account which have all the rights and permissions all the time. Use the account which has read only permissions if there are no modification required. Use policy based management to prevent changes which are accidental. If there was policy of valid names, the accidental change of the table was not possible unless it was intentional delibarate changes. Have a proper auditing of the system in place. You can use DDL triggers but be careful with its usage (get it reviewed properly first). (Add your suggestion here) I guess Method 5 will work all the time (using point in time restore). Everything else is chance of luck and if you are lucky are bad – you will get further incorrect name. Now go back and read the first line of this blog. Out of five method four methods are just lucky guesses. The method 5 will work but again it is a lengthy process if the size of the database is huge or if you do not have full backup. Did I miss anything obvious? Please leave a comment and I will publish your answer with due credit. Reference: Pinal Dave (http://blog.sqlauthority.com) Filed under: PostADay, SQL, SQL Authority, SQL Puzzle, SQL Query, SQL Server, SQL Tips and Tricks, T SQL, Technology

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• Computer Networks UNISA - Chap 14 &ndash; Insuring Integrity &amp; Availability

  - by MarkPearl

  After reading this section you should be able to Identify the characteristics of a network that keep data safe from loss or damage Protect an enterprise-wide network from viruses Explain network and system level fault tolerance techniques Discuss issues related to network backup and recovery strategies Describe the components of a useful disaster recovery plan and the options for disaster contingencies What are integrity and availability? Integrity – the soundness of a networks programs, data, services, devices, and connections Availability – How consistently and reliably a file or system can be accessed by authorized personnel A number of phenomena can compromise both integrity and availability including… security breaches natural disasters malicious intruders power flaws human error users etc Although you cannot predict every type of vulnerability, you can take measures to guard against the most damaging events. The following are some guidelines… Allow only network administrators to create or modify NOS and application system users. Monitor the network for unauthorized access or changes Record authorized system changes in a change management system’ Install redundant components Perform regular health checks on the network Check system performance, error logs, and the system log book regularly Keep backups Implement and enforce security and disaster recovery policies These are just some of the basics… Malware Malware refers to any program or piece of code designed to intrude upon or harm a system or its resources. Types of Malware… Boot sector viruses Macro viruses File infector viruses Worms Trojan Horse Network Viruses Bots Malware characteristics Some common characteristics of Malware include… Encryption Stealth Polymorphism Time dependence Malware Protection There are various tools available to protect you from malware called anti-malware software. These monitor your system for indications that a program is performing potential malware operations. A number of techniques are used to detect malware including… Signature Scanning Integrity Checking Monitoring unexpected file changes or virus like behaviours It is important to decide where anti-malware tools will be installed and find a balance between performance and protection. There are several general purpose malware policies that can be implemented to protect your network including… Every compute in an organization should be equipped with malware detection and cleaning software that regularly runs Users should not be allowed to alter or disable the anti-malware software Users should know what to do in case the anti-malware program detects a malware virus Users should be prohibited from installing any unauthorized software on their systems System wide alerts should be issued to network users notifying them if a serious malware virus has been detected. Fault Tolerance Besides guarding against malware, another key factor in maintaining the availability and integrity of data is fault tolerance. Fault tolerance is the ability for a system to continue performing despite an unexpected hardware or software malfunction. Fault tolerance can be realized in varying degrees, the optimal level of fault tolerance for a system depends on how critical its services and files are to productivity. Generally the more fault tolerant the system, the more expensive it is. The following describe some of the areas that need to be considered for fault tolerance. Environment (Temperature and humidity) Power Topology and Connectivity Servers Storage Power Typical power flaws include Surges – a brief increase in voltage due to lightening strikes, solar flares or some idiot at City Power Noise – Fluctuation in voltage levels caused by other devices on the network or electromagnetic interference Brownout – A sag in voltage for just a moment Blackout – A complete power loss The are various alternate power sources to consider including UPS’s and Generators. UPS’s are found in two categories… Standby UPS – provides continuous power when mains goes down (brief period of switching over) Online UPS – is online all the time and the device receives power from the UPS all the time (the UPS is charged continuously) Servers There are various techniques for fault tolerance with servers. Server mirroring is an option where one device or component duplicates the activities of another. It is generally an expensive process. Clustering is a fault tolerance technique that links multiple servers together to appear as a single server. They share processing and storage responsibilities and if one unit in the cluster goes down, another unit can be brought in to replace it. Storage There are various techniques available including the following… RAID Arrays NAS (Storage (Network Attached Storage) SANs (Storage Area Networks) Data Backup A backup is a copy of data or program files created for archiving or safekeeping. Many different options for backups exist with various media including… These vary in cost and speed. Optical Media Tape Backup External Disk Drives Network Backups Backup Strategy After selecting the appropriate tool for performing your servers backup, devise a backup strategy to guide you through performing reliable backups that provide maximum data protection. Questions that should be answered include… What data must be backed up At what time of day or night will the backups occur How will you verify the accuracy of the backups Where and for how long will backup media be stored Who will take responsibility for ensuring that backups occurred How long will you save backups Where will backup and recovery documentation be stored Different backup methods provide varying levels of certainty and corresponding labour cost. There are also different ways to determine which files should be backed up including… Full backup – all data on all servers is copied to storage media Incremental backup – Only data that has changed since the last full or incremental backup is copied to a storage medium Differential backup – Only data that has changed since the last backup is coped to a storage medium Disaster Recovery Disaster recovery is the process of restoring your critical functionality and data after an enterprise wide outage has occurred. A disaster recovery plan is for extreme scenarios (i.e. fire, line fault, etc). A cold site is a place were the computers, devices, and connectivity necessary to rebuild a network exist but they are not appropriately configured. A warm site is a place where the computers, devices, and connectivity necessary to rebuild a network exists with some appropriately configured devices. A hot site is a place where the computers, devices, and connectivity necessary to rebuild a network exists and all are appropriately configured.

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• SQL SERVER – Backing Up and Recovering the Tail End of a Transaction Log – Notes from the Field #042

  - by Pinal Dave

  [Notes from Pinal]: The biggest challenge which people face is not taking backup, but the biggest challenge is to restore a backup successfully. I have seen so many different examples where users have failed to restore their database because they made some mistake while they take backup and were not aware of the same. Tail Log backup was such an issue in earlier version of SQL Server but in the latest version of SQL Server, Microsoft team has fixed the confusion with additional information on the backup and restore screen itself. Now they have additional information, there are a few more people confused as they have no clue about this. Previously they did not find this as a issue and now they are finding tail log as a new learning. Linchpin People are database coaches and wellness experts for a data driven world. In this 42nd episode of the Notes from the Fields series database expert Tim Radney (partner at Linchpin People) explains in a very simple words, Backing Up and Recovering the Tail End of a Transaction Log. Many times when restoring a database over an existing database SQL Server will warn you about needing to make a tail end of the log backup. This might be your reminder that you have to choose to overwrite the database or could be your reminder that you are about to write over and lose any transactions since the last transaction log backup. You might be asking yourself “What is the tail end of the transaction log”. The tail end of the transaction log is simply any committed transactions that have occurred since the last transaction log backup. This is a very crucial part of a recovery strategy if you are lucky enough to be able to capture this part of the log. Most organizations have chosen to accept some amount of data loss. You might be shaking your head at this statement however if your organization is taking transaction logs backup every 15 minutes, then your potential risk of data loss is up to 15 minutes. Depending on the extent of the issue causing you to have to perform a restore, you may or may not have access to the transaction log (LDF) to be able to back up those vital transactions. For example, if the storage array or disk that holds your transaction log file becomes corrupt or damaged then you wouldn’t be able to recover the tail end of the log. If you do have access to the physical log file then you can still back up the tail end of the log. In 2013 I presented a session at the PASS Summit called “The Ultimate Tail Log Backup and Restore” and have been invited back this year to present it again. During this session I demonstrate how you can back up the tail end of the log even after the data file becomes corrupt. In my demonstration I set my database offline and then delete the data file (MDF). The database can’t become more corrupt than that. I attempt to bring the database back online to change the state to RECOVERY PENDING and then backup the tail end of the log. I can do this by specifying WITH NO_TRUNCATE. Using NO_TRUNCATE is equivalent to specifying both COPY_ONLY and CONTINUE_AFTER_ERROR. It as its name says, does not try to truncate the log. This is a great demo however how could I achieve backing up the tail end of the log if the failure destroys my entire instance of SQL and all I had was the LDF file? During my demonstration I also demonstrate that I can attach the log file to a database on another instance and then back up the tail end of the log. If I am performing proper backups then my most recent full, differential and log files should be on a server other than the one that crashed. I am able to achieve this task by creating new database with the same name as the failed database. I then set the database offline, delete my data file and overwrite the log with my good log file. I attempt to bring the database back online and then backup the log with NO_TRUNCATE just like in the first example. I encourage each of you to view my blog post and watch the video demonstration on how to perform these tasks. I really hope that none of you ever have to perform this in production, however it is a really good idea to know how to do this just in case. It really isn’t a matter of “IF” you will have to perform a restore of a production system but more of a “WHEN”. Being able to recover the tail end of the log in these sever cases could be the difference of having to notify all your business customers of data loss or not. If you want me to take a look at your server and its settings, or if your server is facing any issue we can Fix Your SQL Server. Note: Tim has also written an excellent book on SQL Backup and Recovery, a must have for everyone. Reference: Pinal Dave (http://blog.sqlauthority.com)Filed under: Notes from the Field, PostADay, SQL, SQL Authority, SQL Performance, SQL Query, SQL Server, SQL Tips and Tricks, T SQL

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• Determining the angle to fire a shot when target and shooter moves, and bullet moves with shooter velocity added in

  - by Azaral

  I saw this question: Predicting enemy position in order to have an object lead its target and followed the link in the answer to stack overflow. In the stack overflow page I used the 2nd answer, the one that is a large mathematical derivation. My situation is a little different though. My first question though is will the answer provided in the stack overflow page even work to begin with, assuming the original circumstances of moving target and stationary shooter. My situation is a little different than that situation. My target moves, the shooter moves, and the bullets from the shooter start off with the velocities in x and y added to the bullets' x and y velocities. If you are sliding to the right, the bullets will remain in front of you as you move so as long as your velocity remains constant. What I'm trying to do is to get the enemy to be able to determine where they need to shoot in order to hit the player. Unless the player and enemy is stationary, the velocity from the ship adding to the velocity of the bullets will cause a miss. I'd rather like to prevent that. I used the formula in the stack overflow answer and did what I thought were the appropriate adjustments. I've been banging at this for the last four hours and I just can't make it click. It is probably something really simple and boneheaded that I am missing (that seems to be a lot of my problems lately). Here is the solution presented from the stack overflow answer: It boils down to solving a quadratic equation of the form: a * sqr(x) + b * x + c == 0 Note that by sqr I mean square, as opposed to square root. Use the following values: a := sqr(target.velocityX) + sqr(target.velocityY) - sqr(projectile_speed) b := 2 * (target.velocityX * (target.startX - cannon.X) + target.velocityY * (target.startY - cannon.Y)) c := sqr(target.startX - cannon.X) + sqr(target.startY - cannon.Y) Now we can look at the discriminant to determine if we have a possible solution. disc := sqr(b) - 4 * a * c If the discriminant is less than 0, forget about hitting your target -- your projectile can never get there in time. Otherwise, look at two candidate solutions: t1 := (-b + sqrt(disc)) / (2 * a) t2 := (-b - sqrt(disc)) / (2 * a) Note that if disc == 0 then t1 and t2 are equal. If there are no other considerations such as intervening obstacles, simply choose the smaller positive value. (Negative t values would require firing backward in time to use!) Substitute the chosen t value back into the target's position equations to get the coordinates of the leading point you should be aiming at: aim.X := t * target.velocityX + target.startX aim.Y := t * target.velocityY + target.startY Here is my code, after being corrected by Sam Hocevar (thank you again for your help!). It still doesn't work. For some reason it never enters the section of code inside the if(disc = 0) (obviously because it is always less than zero but...). However, if I plug the numbers from my game log on the enemy and player positions and velocities it outputs a valid firing solution. I have looked at the code side by side a couple of times now and I can't find any differences. There has got to be something simple I'm missing here. If someone else could look at this code and determine what is going on here I'd appreciate it. I know it's not going through that section because if it were, shouldShoot would become true and the enemy would be blasting away at the player. This section calls the function in question, CalculateShootHeading() if(shouldMove) { UseEngines(); } x += xVelocity; y += yVelocity; CalculateShootHeading(); if(shouldShoot) { ShootWeapons(); } UpdateWeapons(); This is CalculateShootHeading(). This is inside the enemy class so x and y are the enemy's x and y and the same with velocity. One output from my game log gives Player X = 2108, Player Y = -180.956, Player X velocity = 10.9949, Player Y Velocity = -6.26017, Enemy X = 1988.31, Enemy Y = -339.051, Enemy X velocity = 1.81666, Enemy Y velocity = -9.67762, 0 enemy projectiles. The output from the console tester is Bullet position = 2210.49, -239.313 and Player Position = 2210.49, -239.313. This doesn't make any sense. The only thing that could be different is the code or the input into my function in the game and I've checked that and I don't think that it is wrong as it's updated before this and never changed. float const bulletSpeed = 30.f; float const dx = playerX - x; float const dy = playerY - y; float const vx = playerXVelocity - xVelocity; float const vy = playerYVelocity - yVelocity; float const a = vx * vx + vy * vy - bulletSpeed * bulletSpeed; float const b = 2.f * (vx * dx + vy * dy); float const c = dx * dx + dy * dy; float const disc = b * b - 4.f * a * c; shouldShoot = false; if (disc >= 0.f) { float t0 = (-b - std::sqrt(disc)) / (2.f * a); float t1 = (-b + std::sqrt(disc)) / (2.f * a); if (t0 < 0.f || (t1 < t0 && t1 >= 0.f)) { t0 = t1; } if (t0 >= 0.f) { float shootx = vx + dx / t0; float shooty = vy + dy / t0; heading = std::atan2(shooty, shootx) * RAD2DEGREE; } shouldShoot = true; }

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