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  • Math behind multivariate testing for website optimization

    - by corkjack
    I am looking for theoretical resources (books, tutorials, etc.) to learn about making sound statistical inferences given (plenty of) multivariate website conversion data. I'm after the math involved, and cannot find any good non-marketing stuff on the web. The sort of questions I want to answer: how much impact does a single variable (e.g. color of text) have? what is the correlation between variables? what type of distribution is used for modelling (Gaussian, Binomial, etc.)? When using statistics to analyze results - what should be considered as a random variable - the web-page element that gets different variations or the binary conversion-or-no-conversion outcome of an impression? There's plenty of information about different website optimization testing methods and their benefits\pitfalls, plenty of information about multivariate statistics in general, do you guys know of resources that discuss statistics in this specific context of website optimization ? Thanks for any info!

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  • PHP Round function

    - by Steve
    Is it possible to round a number where if it's 5 , just leave it , anything below 5 round down , anything above 5 round up? EX: 5 * 1.35 = 6.75 .... leave it 5.2 * 1.35 = 7.02 .... 7.00 5.5 * 1.35 = 7.56 .... 8.00 I've formatted with round($n,0, PHP_ROUND_HALF_UP) where $n is the product from the above calc , which leaves 6.75 but returns 7.02 for the next one. I also tried round($n,-1, PHP_ROUND_HALF_UP) which gives me the 7.00 on the second calc but then of course won't return a 6.75 for the first, instead it returns 680. This is a ticket markup calculation where the user enters the first number and is multiplied by the second. I actually remove the decimal because they don't want to see it, and they want this sort of customized rounding on the result. Thanks, Steve

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  • In 3D camera math, calculate what Z depth is pixel unity for a given FOV

    - by badweasel
    I am working in iOS and OpenGL ES 2.0. Through trial and error I've figured out a frustum to where at a specific z depth pixels drawn are 1 to 1 with my source textures. So 1 pixel in my texture is 1 pixel on the screen. For 2d games this is good. Of course it means that I also factor in things like the size of the quad and the size of the texture. For example if my sprite is a quad 32x32 pixels. The quad size is 3.2 units wide and tall. And the texcoords are 32 / the size of the texture wide and tall. Then the frustum is: matrixFrustum(-(float)backingWidth/frustumScale,(float)backingWidth/frustumScale, -(float)backingHeight/frustumScale, (float)backingHeight/frustumScale, 40, 1000, mProjection); Where frustumScale is 800 for a retina screen. Then at a distance of 800 from camera the sprite is pixel for pixel the same as photoshop. For 3d games sometimes I still want to be able to do this. But depending on the scene I sometimes need the FOV to be different things. I'm looking for a way to figure out what Z depth will achieve this same pixel unity for a given FOV. For this my mProjection is set using: matrixPerspective(cameraFOV, near, far, (float)backingWidth / (float)backingHeight, mProjection); With testing I found that at an FOV of 45.0 a Z of 38.5 is very close to pixel unity. And at an FOV of 30.0 a Z of 59.5 is about right. But how can I calculate a value that is spot on? Here's my matrixPerspecitve code: void matrixPerspective(float angle, float near, float far, float aspect, mat4 m) { //float size = near * tanf(angle / 360.0 * M_PI); float size = near * tanf(degreesToRadians(angle) / 2.0); float left = -size, right = size, bottom = -size / aspect, top = size / aspect; // Unused values in perspective formula. m[1] = m[2] = m[3] = m[4] = 0; m[6] = m[7] = m[12] = m[13] = m[15] = 0; // Perspective formula. m[0] = 2 * near / (right - left); m[5] = 2 * near / (top - bottom); m[8] = (right + left) / (right - left); m[9] = (top + bottom) / (top - bottom); m[10] = -(far + near) / (far - near); m[11] = -1; m[14] = -(2 * far * near) / (far - near); } And my mView is set using: lookAtMatrix(cameraPos, camLookAt, camUpVector, mView); * UPDATE * I'm going to leave this here in case anyone has a different solution, can explain how they do it, or why this works. This is what I figured out. In my system I use a 10th scale unit to pixels on non-retina displays and a 20th scale on retina displays. The iPhone is 640 pixels wide on retina and 320 pixels wide on non-retina (obsolete). So if I want something to be the full screen width I divide by 20 to get the OpenGL unit width. Then divide that by 2 to get the left and right unit position. Something 32 units wide centered on the screen goes from -16 to +16. Believe it or not I have an excel spreadsheet do all this math for me and output all the vertex data for my sprite sheet. It's an arbitrary thing I made up to do .1 units = 1 non-retina pixel or 2 retina pixels. I could have made it .01 units = 2 pixels and someday I might switch to that. But for now it's the other. So the width of the screen in units is 32.0, and that means the left most pixel is at -16.0 and the right most is at 16.0. After messing a bit I figured out that if I take the [0] value of an identity modelViewProjection matrix and multiply it by 16 I get the depth required to get 1:1 pixels. I don't know why. I don't know if the 16 is related to the screen size or just a lucky guess. But I did a test where I placed a sprite at that calculated depth and varied the FOV through all the valid values and the object stays steady on screen with 1:1 pixels. So now I'm just calculating the unityDepth that way. If someone gives me a better answer I'll checkmark it.

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  • Documenting mathematical logic in code

    - by Kiril Raychev
    Sometimes, although not often, I have to include math logic in my code. The concepts used are mostly very simple, but the resulting code is not - a lot of variables with unclear purpose, and some operations with not so obvious intent. I don't mean that the code is unreadable or unmaintainable, just that it's waaaay harder to understand than the actual math problem. I try to comment the parts which are hardest to understand, but there is the same problem as in just coding them - text does not have the expressive power of math. I am looking for a more efficient and easy to understand way of explaining the logic behind some of the complex code, preferably in the code itself. I have considered TeX - writing the documentation and generating it separately from the code. But then I'd have to learn TeX, and the documentation will not be in the code itself. Another thing I thought of is taking a picture of the mathematical notations, equations and diagrams written on paper/whiteboard, and including it in javadoc. Is there a simpler and clearer way? P.S. Giving descriptive names(timeOfFirstEvent instead of t1) to the variables actually makes the code more verbose and even harder too read.

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  • Best way to calculate unit deaths in browser game combat?

    - by MikeCruz13
    My browser game's combat system is written and mechanically functioning well. It's written in PHP and uses a SQL database. I'm happy with the unit balance in relation to one another. I am, however, a little worried about how I'm calculating unit deaths when one player attacks another because the deaths seem to pile up a little fast for my taste. For this system, a battle doesn't just trigger, calculate winner, and end. Instead, it is allowed to go for several rounds (say one round every 15 mins.) until one side passes a threshold of being too strong for the other player and allows players to send reinforcements between rounds. Each round, units pair up and attack each other. Essentially what I do is calculate the damage: AP = Attack Points HP = Hit Points Units AP * Quantity * Random Factors * other factors (such as attrition) I take that and divide by the defending unit's HP to find the number of casualties of defending units. So, for example (simplified to take out some factors), if I have: 500 attackers with 50 AP vs 1000 defenders with 100 HP = 250 deaths. I wonder if that last step could be handled better to reduce the deaths piling up. Some ideas: I just change all the units with more HP? I make sure to set the Attacking unit's AP to be a max of the defender's HP to make sure they only kill 1 unit. (is that fair if I have less huge units vs many small units?) I spread the damage around more by including the defending unit's quantity more? i.e. in that scenario some are dead and some are 50% damage. (How would I track this every round?) Other better mathematical approaches?

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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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  • Round-Robin DNS in mobile networks

    - by k7k0
    After reading load distribution alternatives and giving my limited skills on the area I'm biased toward round-robin DNS strategy. From what I understood, one key aspect of DNS Round-Robin is setting a low TTL value, avoiding caching. My main concern is that all my traffic comes from mobile networks, almost 30% of that comes from t-mobile 3G. Some questions: 1) Is there a chance that almost all clients on the same mobile network will be redirected to the same IP in the TTL frame? That would kill the distribution technique. 2) If I choose a really low TTL (zero or one). That impacts directly over client performance? It does a DNS miss every time or it's a setting that only impacts on DNS servers? Any help would be much appreciated. Thanks

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  • Excel: ROUND & MOD giving me strange DATE results

    - by Mike
    This is sort of related to a previous question. My formula, which seemed to work fine yesterday now gives strange results. Today is the 30th of March (30/03/10). It's 10:11am on the clock that the computer is using for the time stamp in the NOW() part of my worksheet. Below is the formula and a screen shot of the results/columns. QUESTION: Why ddoes it show 1/2 day, and also where does 23 1/2 come from? The NOW() is in a hidden column (F2)...which I forgot to unhide before I took the screen shot. =IF(ISBLANK(I2),ROUND(MOD(H2-F2,24),2),ROUND(MOD(I2-F2,24),2)) Thanks Mike

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  • Round prices up to nearest 5 after conversion in oscommerce

    - by Rhyso
    Hi there, A conversion question relating to prices in oscommerce: I am needing for a custom currency conversion to round the USD prices up to the nearest 5$ to avoid prices being displayed at silly prices such as $263. I am trying to convert to an int and round the following line : $curr-display_price($listing['products_price'], tep_get_tax_rate($listing['products_tax_class_id'])); ( as for some reason the price is displayed as a string, im guessing to include the currency sign) However not having much luck. Does anybody know where the root conversion takes place as it might be easier for me to round() or ceil() from there when it is a raw integer Or any other ideas of how I can round the conversion? Thanks for any help Rhys Thomas

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  • Avoid compiling when using Decimal.Round() method (C#/CF)

    - by Christian Almeida
    Is there a way to tell to VS2005 to get compiler error when using "some defined" method? It probably sounds strange, but I do not want to compile when using Decimal.Round(). Reason: CF does not round by "awayfromzero", so I created a method to do this job. But sometimes I (and team) forget that is not to use Decimal.Round. So I'd like to get a compiler error when using it.

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  • How to integer-divide round negative numbers *down*?

    - by Conrad Albrecht
    Seems like whenever I divide a negative int by a positive int, I need it to round down (toward -inf), not toward 0. But both C# and C++ round toward 0. So I guess I need a DivideDownward() method. I can write it in a few lines with a test for negative and so on, but my ideas seem klugey. So I'm wondering if I'm missing something and if you have an "elegant" way to round negative division downward.

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  • Monitoring Your Servers

    - by Grant Fritchey
    If you are the DBA in a large scale enterprise, you’re probably already monitoring your servers for up-time and performance. But if you work for a medium-sized business, a small shop, or even a one-man operation, chances are pretty good that you’re not doing that sort of monitoring. You know that you’re supposed to be doing it, but other things, more important at-the-moment things, keep getting in the way. After all, which is more important, some monitoring or backup testing?  Backup testing, of course. Monitoring is frequently one of those things that you do when can get around to it.  Well, as you can see at the right, I have your round tuit ready to go. What if I told you that you could get monitoring on your servers for up-time, job completion, performance, all the standard stuff? And what if I told you that you wouldn’t need to install and configure another server in your environment to get it done? And what if I told you that you’d be able to set up and customize your alerts so you could know if your server was offline or a drive was full? Almost nothing for you to do, and you’ll have a full-blown monitoring process. Sounds to good to be true doesn’t it? Well, it’s coming. We’re creating an online, remote, monitoring system here at Red Gate. You’ll be able to use our SQL Monitor tool (which you can see here, monitoring SQL Server Central in real time) to keep track of your systems, but without having to set up a server and a database for storing the information collected. Instead, we’re taking advantage of services available through the internet to enable collection and storage of this information remotely, off your systems. All you have to do is install a piece of software that will communicate between our service and your servers and you’ll be off and running. It’s that easy. Before you get too excited, let me break the news that this is the near future I’m talking about. We’re setting up the program and there’s a sign-up you can use to get in on the initial tests.

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  • Some date math fun

    - by drsql
    Note: This concept presented is pretty simple and I am not claiming that I am the first to do this… so if you were the one who came up with this, let me know and I will give you linkage Today I was needing to get the data for the current month for a query, and it hit me that I really didn’t have a good way to do this.  There were two common methods that people use: WHERE YEAR(MonthColumn) = YEAR(Getdate()) AND MONTH(MonthColumn) = MONTH(Getdate()) But this particular method is pretty horrible...(read more)

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  • Some date math fun

    - by drsql
    Note: This concept presented is pretty simple and I am not claiming that I am the first to do this… so if you were the one who came up with this, let me know and I will give you linkage Today I was needing to get the data for the current month for a query, and it hit me that I really didn’t have a good way to do this.  There were two common methods that people use: WHERE YEAR(MonthColumn) = YEAR(Getdate()) AND MONTH(MonthColumn) = MONTH(Getdate()) But this particular method is pretty horrible...(read more)

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  • as3 3D camera lookat

    - by Johannes Jensen
    I'm making a 3D camera scene in Flash, draw using drawTriangles() and rotated and translated using a Matrix3D. I've got the camera to look after a specific point, but only on the Y-axis, using the x and z coordinates, here is my code so far: var dx:Number = camera.x - lookAt.x; var dy:Number = camera.y - lookAt.y; var dz:Number = camera.z - lookAt.z; camera.rotationY = Math.atan2(dz, dx) * (180 / Math.PI) + 270; so no matter the x or z position, the point is always on the mid of the screen, IF and only if y matches with the camera. So what I need is to calculate the rotationX (which are measured in degrees not radians), and I was wondering how I would do this?

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  • Circular Bullet Spread not Even

    - by SoulBeaver
    I'm creating a bullet shooter much in the style of Touhou. Right now I want to have a very simple circular shot being fired from the enemy. See this picture: As you can see, the spacing is very uneven, which isn't very good if you want to survive. The code I'm using is this: private function shoot() : void { const BULLETS_PER_WAVE : int = 72; var interval : Number = BULLETS_PER_WAVE / 360; for (var i : int = 0; i < BULLETS_PER_WAVE; ++i { var xSpeed : Number = GameConstants.BULLET_NORMAL_SPEED_X * Math.sin(i * interval); var ySpeed : Number = GameConstants.BULLET_NORMAL_SPEED_Y * Math.cos(i * interval); BulletFactory.createNormalBullet(bulletColor_, alice_.center, xSpeed, ySpeed); } canShoot_ = false; cooldownTimer_.start(); } I imagine my mistake is in the sin, cos functions, but I'm not entirely sure what's wrong.

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  • Math with Timestamp

    - by Knut Vatsendvik
    table.sql { border-width: 1px; border-spacing: 2px; border-style: dashed; border-color: #0023ff; border-collapse: separate; background-color: white; } table.sql th { border-width: 1px; padding: 1px; border-style: none; border-color: gray; background-color: white; -moz-border-radius: 0px 0px 0px 0px; } table.sql td { border-width: 1px; padding: 3px; border-style: none; border-color: gray; background-color: white; -moz-border-radius: 0px 0px 0px 0px; } .sql-keyword { color: #0000cd; background-color: inherit; } .sql-result { color: #458b74; background-color: inherit; } Got this little SQL quiz from a colleague.  How to add or subtract exactly 1 second from a Timestamp?  Sounded simple enough at first blink, but was a bit trickier than expected. If the data type had been a Date, we knew that we could add or subtract days, minutes or seconds using + or – sysdate + 1 to add one day sysdate - (1 / 24) to subtract one hour sysdate + (1 / 86400) to add one second Would the same arithmetic work with Timestamp as with Date? Let’s test it out with the following query SELECT   systimestamp , systimestamp + (1 / 86400) FROM dual; ---------- 03.05.2010 22.11.50,240887 +02:00 03.05.2010 The first result line shows us the system time down to fractions of seconds. The second result line shows the result as Date (as used for date calculation) meaning now that the granularity is reduced down to a second.   By using the PL/SQL dump() function, we can confirm this with the following query SELECT   dump(systimestamp) , dump(systimestamp + (1 / 86400)) FROM dual; ---------- Typ=188 Len=20: 218,7,5,4,8,53,9,0,200,46,89,20,2,0,5,0,0,0,0,0 Typ=13 Len=8: 218,7,5,4,10,53,10,0 Where typ=13 is a runtime representation for Date. So how can we increase the precision to include fractions of second? After investigating it a bit, we found out that the interval data type INTERVAL DAY TO SECOND could be used with the result of addition or subtraction being a Timestamp. Let’s try again our first query again, now using the interval data type. SELECT systimestamp,    systimestamp + INTERVAL '0 00:00:01.0' DAY TO SECOND(1) FROM dual; ---------- 03.05.2010 22.58.32,723659000 +02:00 03.05.2010 22.58.33,723659000 +02:00 Yes, it worked! To finish the story, here is one example showing how to specify an interval of 2 days, 6 hours, 30 minutes, 4 seconds and 111 thousands of a second. INTERVAL ‘2 6:30:4.111’ DAY TO SECOND(3)

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  • Time passage arithmetic explanation

    - by Cyber Axe
    I ported this from http://www.effectgames.com/effect/article.psp.html/joe/Old_School_Color_Cycling_with_HTML5 some time ago. However i'm now wanting to modify it for the purpose of changing it from floating point to fixed point maths for enhanced efficiency (for those who are going to talk about premature optimization and what not, i want to have my entire engine in fixed point both as a learning process for me and so i can port code more easily to systems in the future that dont have native floating points such as arm cpus) My initial conversion to fixed points just resulted in the cycling stuck on either the first or last frame of cycling. Plus it would be nice to understand better how it works so i can add more options and so forth in the future, my maths however sucks and the comments are limited so i don't really know how the maths work for determining the frame it shoud use (cycleAmount) I was also a beginner when i ported it as i had no idea between floating points and integers and what not. So in summary my question is, can anyone give an explination of the arithmatic used for determining the cycleAmount (which determings the "frame" of the cycle) This is the working floating point maths version of the code: public final void cycle(Colour[] sourceColours, double timeNow, double speedAdjust) { // Cycle all animated colour ranges in palette based on timestamp. sourceColours = sourceColours.clone(); int cycleSize; double cycleRate; double cycleAmount; Cycle cycle; for (int i = 0, len = cycles.length; i < len; ++i) { cycle = cycles[i]; cycleSize = (cycle.HIGH - cycle.LOW) + 1; cycleRate = cycle.RATE / (int) (CYCLE_SPEED / speedAdjust); cycleAmount = 0; if (cycle.REVERSE < 3) { // Standard Cycle cycleAmount = DFLOAT_MOD((timeNow / (1000 / cycleRate)), cycleSize); if (cycle.REVERSE < 1) { cycleAmount = cycleSize - cycleAmount; // If below 1 make sure its not reversed. } } else if (cycle.REVERSE == 3) { // Ping-Pong cycleAmount = DFLOAT_MOD((timeNow / (1000 / cycleRate)), cycleSize << 1); if (cycleAmount >= cycleSize) { cycleAmount = (cycleSize * 2) - cycleAmount; } } else if (cycle.REVERSE < 6) { // Sine Wave cycleAmount = DFLOAT_MOD((timeNow / (1000 / cycleRate)), cycleSize); cycleAmount = Math.sin((cycleAmount * 3.1415926 * 2) / cycleSize) + 1; if (cycle.REVERSE == 4) { cycleAmount *= (cycleSize / 4); } else if (cycle.REVERSE == 5) { cycleAmount *= (cycleSize >> 1); } } if (cycle.REVERSE == 2) { reverseColours(sourceColours, cycle); } if (USE_BLEND_SHIFT) { blendShiftColours(sourceColours, cycle, cycleAmount); } else { shiftColours(sourceColours, cycle, cycleAmount); } if (cycle.REVERSE == 2) { reverseColours(sourceColours, cycle); } } colours = sourceColours; } // This utility function allows for variable precision floating point modulus. private double DFLOAT_MOD(final double d, final double b) { return (Math.floor(d * PRECISION) % Math.floor(b * PRECISION)) / PRECISION; }

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