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Search found 562 results on 23 pages for 'discrete mathematics'.

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  • Encode complex number as RGB pixel and back

    - by Vi
    How is it better to encode a complex number into RGB pixel and vice versa? Probably (logarithm of) an absolute value goes to brightness and an argument goes to hue. Desaturated pixes should receive randomized argument in reverse transformation. Something like: 0 - (0,0,0) 1 - (255,0,0) -1 - (0,255,255) 0.5 - (128,0,0) i - (255,255,0) -i - (255,0,255) (0,0,0) - 0 (255,255,255) - e^(i * random) (128,128,128) - 0.5 * e^(i *random) (0,128,128) - -0.5 Are there ready-made formulas for that? Edit: Looks like I just need to convert RGB to HSB and back. Edit 2: Existing RGB - HSV converter fragment: if (hsv.sat == 0) { hsv.hue = 0; // ! return hsv; } I don't want 0. I want random. And not just if hsv.sat==0, but if it is lower that it should be ("should be" means maximum saturation, saturation that is after transformation from complex number).

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  • finding ALL cycles in a huge sparse matrix

    - by Andy
    Hi there, First of all I'm quite a Java beginner, so I'm not sure if this is even possible! Basically I have a huge (3+million) data source of relational data (i.e. A is friends with B+C+D, B is friends with D+G+Z (but not A - i.e. unmutual) etc.) and I want to find every cycle within this (not necessarily connected) directed graph. I've found this thread (http://stackoverflow.com/questions/546655/finding-all-cycles-in-graph/549402#549402) which has pointed me to Donald Johnson's (elementary) cycle-finding algorithm which, superficially at least, looks like it'll do what I'm after (I'm going to try when I'm back at work on Tuesday - thought it wouldn't hurt to ask in the meanwhile!). I had a quick scan through the code of the Java implementation of Johnson's algorithm (in that thread) and it looks like a matrix of relations is the first step, so I guess my questions are: a) Is Java capable of handling a 3+million*3+million matrix? (was planning on representing A-friends-with-B by a binary sparse matrix) b) Do I need to find every connected subgraph as my first problem, or will cycle-finding algorithms handle disjoint data? c) Is this actually an appropriate solution for the problem? My understanding of "elementary" cycles is that in the graph below, rather than picking out A-B-C-D-E-F it'll pick out A-B-F, B-C-D etc. but that's not the end of the world given the task. E / \ D---F / \ / \ C---B---A d) If necessary, I can simplify the problem by enforcing mutuality in relations - i.e. A-friends-with-B <== B-friends-with-A, and if really necessary I can maybe cut down the data size, but realistically it is always going to be around the 1mil mark. z) Is this a P or NP task?! Am I biting off more than I can chew? Thanks all, any help appreciated! Andy

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  • What most efficient method to find a that triangle which contains the given point?

    - by Christo
    Given the triangle with vertices (a,b,c): c / \ / \ / \ a - - - b Which is then subdivided into four triangles by halving each of the edges: c / \ / \ ca / \ bc /\ - - - /\ / \ / \ / \ / \ a- - - - ab - - - -b Wich results in four triangles (a, ab, ca), (b, bc, ab), (c, ca, bc), (ab, bc, ca). Now given a point p. How do I determine in which triangle p lies, given that p is within the outer triangle (a, b, c)? Currently I intend to use ab as the origin. Check whether it is to the left of right of the line "ca - ab" using the perp of "ca - ab" and checking the sign against the dot product of "ab - a" and the perp vector and the vector "p - ab". If it is the same or the dot product is zero then it must be in (a, ab, ca)... Continue with this procedure with the other outer triangles (b, ba, ab) & (c, ca, ba). In the end if it didn't match with these it must be contained within the inner triangle (ab, bc, ca). Is there a better way to do it?

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  • Perturb vector by some angle

    - by Myx
    Hello: I have a unit vector in 3D space whose direction I wish to perturb by some angle within the range 0 to theta, with the position of the vector remaining the same. What is a way I can accomplish this? Thanks.

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  • How many times can you randomly generate a GUID before you risk duplicates? (.NET)

    - by SLC
    Mathematically I suppose it's possible that even two random GUIDs generated using the built in method in the .NET framework are identical, but roughly how likely are they to clash if you generate hundreds or thousands? If you generated one for every copy of Windows in the world, would they clash? The reason I ask is because I have a program that creates a lot of objects, and destroys some too, and I am wondering about the likelihood of any of those objects (including the destroyed ones) having identical GUIDs.

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  • how to find distinct digit set numbers over a range of integers?

    - by evil.coder
    Suppose i have a unsigned integer, call it low and one another call it high such that highlow. The problem is to find distinct digit set numbers over this range. For example, suppose low is 1 and high is 20 then the answer is 20, because all the numbers in this range are of distinct digit sets. If suppose low is 1 and high is 21, then the answer is 20, because 12 and 21 have same digit set i.e.1, 2. I am not looking for a bruteforce algo., if anyone has a better solution then a usual bruteforce approach, please tell..

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  • How can you transform a set of numbers into mostly whole ones?

    - by Alice
    Small amount of background: I am working on a converter that bridges between a map maker (Tiled) that outputs in XML, and an engine (Angel2D) that inputs lua tables. Most of this is straight forward However, Tiled outputs in pixel offsets (integers of absolute values), while Angel2D inputs OpenGL units (floats of relative values); a conversion factor between these two is needed (for example, 32px = 1gu). Since OpenGL units are abstract, and the camera can zoom in or out if the objects are too small or big, the actual conversion factor isn't important; I could use a random number, and the user would merely have to zoom in or out. But it would be best if the conversion factor was selected such that most numbers outputted were small and whole (or fractions of small whole numbers), because that makes it easier to work with (and the whole point of the OpenGL units is that they are easy to work with). How would I find such a conversion factor reliably? My first attempt was to use the smallest number given; this resulted in no fractions below 1, but often lead to lots of decimal places where the factors didn't line up. Then I tried the mode of the sequence, which lead to the largest number of 1's possible, but often lead to very long floats for background images. My current approach gets the GCD of the whole sequence, which, when it works, works great, but can easily be thrown off course by a single bad apple. Note that while I could easily just pass the numbers I am given along, or pick some fixed factor, or use one of the conversions I specified above, I am looking for a method to reliably scale this list of integers to small, whole numbers or simple fractions, because this would most likely be unsurprising to the end user; this is not a one off conversion. The end users tend to use 1.0 as their "base" for manipulations (because it's simple and obvious), so it would make more sense for the sizes of entities to cluster around this.

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

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

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  • Constructing colours for maximum contrast

    - by Martin
    I want to draw some items on screen, each item is in one of N sets. The number of sets changes all the time, so I need to calculate N different colours which are as different as possible (to make it easy to identify what is in which set). So, for example with N = 2 my results would be black and white. With three I guess I would get all red, all green, all blue. For all four, it's less obvious what the correct answer is, and this is where I'm having trouble.

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  • Puzzle related to cake [closed]

    - by Abhi
    Dear All While having tea with one of my colleague at evening time yesterday. He asked me one puzzle related to cake. The puzzle goes this way: Suppose i have a circular cake. And to that cake, I have to cut three times anywhere with maximum number of pieces without bothering abt the equal segment So how many maximum number of pieces it will make? A/c to me, the maximum number of pieces will be 7. But i am not sure. So please can u all tell me how many maximum number of pieces it will make & how? Please answer one at a time..... Thanks in advance...

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  • Resource placement (optimal strategy)

    - by blackened
    I know that this is not exactly the right place to ask this question, but maybe a wise guy comes across and has the solution. I'm trying to write a computer game and I need an algorithm to solve this question: The game is played between 2 players. Each side has 1.000 dollars. There are three "boxes" and each player writes down the amount of money he is going to place into those boxes. Then these amounts are compared. Whoever placed more money in a box scores 1 point (if draw half point each). Whoever scores more points wins his opponents 1.000 dollars. Example game: Player A: [500, 500, 0] Player B: [333, 333, 334] Player A wins because he won Box A and Box B (but lost Box C). Question: What is the optimal strategy to place the money? I have more questions to ask (algorithm related, not math related) but I need to know the answer to this one first. Update (1): After some more research I've learned that these type of problems/games are called Colonel Blotto Games. I did my best and found few (highly technical) documents on the subject. Cutting it short, the problem I have (as described above) is called simple Blotto Game (only three battlefields with symmetric resources). The difficult ones are the ones with, say, 10+ battle fields with non-symmetric resources. All the documents I've read say that the simple Blotto game is easy to solve. The thing is, none of them actually say what that "easy" solution is.

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  • How to find the formula of best case and worst case of my algorithm?

    - by rachel7660
    I was given a task. Write an algorithm so that, the input of 2 lists of data, will have at least one in common. So, this is my algorithm: (I write the code in php) $arrayA = array('5', '6', '1', '2', '7'); $arrayB = array('9', '2', '1', '8', '3'); $arrayC = array(); foreach($arrayA as $val){ if(in_array($val, $arrayB)){ array_push($arrayC, $val); } } Thats my own algo, not sure if its a good one. So, based on my algorithm, how to find the formula of best case and worst case (big O)? Note: Please do let me know, if my algorithm is wrong. My goal is " input of 2 lists of data, will have at least one in common."

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  • Adding to a bit array

    - by Martin
    In my program, I am using BitArrays to represent 160 bit numbers. I want to be able to add, subtract, increment and decrement these numbers, what is the algorithm for doing this? At the moment I'm not interested in multiplication and division, but I might be in the future so bonus points for that. I'm implementing in C#, but pseudocode is fine if you're not familiar with the language

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  • skipping certain number of frames on a timeline

    - by clamp
    hi, i have a mathematical problem which is a bit hard to describe, but i'll give it a try anyway. in a timeline, i have a number of frames, of which i want to skip a certain number of frames, which should be evenly distributed along the timeline. for example i have 10 frames and i want to skip 5, then the solution is easy: we skip every second frame. 10/5 = 2 if (frame%2 == 0) skip(); but what if the above division does result in a floating number? for example in 44 frames i want to skip 15 times. how can i determine the 15 frames which should be skipped? thanks!

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  • Finding a Eulerian Tour

    - by user590903
    I am trying to solve a problem on Udacity described as follows: # Find Eulerian Tour # # Write a function that takes in a graph # represented as a list of tuples # and return a list of nodes that # you would follow on an Eulerian Tour # # For example, if the input graph was # [(1, 2), (2, 3), (3, 1)] # A possible Eulerian tour would be [1, 2, 3, 1] I came up with the following solution, which, while not as elegant as some of the recursive algorithms, does seem to work within my test case. def find_eulerian_tour(graph): tour = [] start_vertex = graph[0][0] tour.append(start_vertex) while len(graph) > 0: current_vertex = tour[len(tour) - 1] for edge in graph: if current_vertex in edge: if edge[0] == current_vertex: current_vertex = edge[1] else: current_vertex = edge[0] graph.remove(edge) tour.append(current_vertex) break return tour graph = [(1, 2), (2, 3), (3, 1)] print find_eulerian_tour(graph) >> [1, 2, 3, 1] However, when submitting this, I get rejected by the grader. I am doing something wrong? I can't see any errors.

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  • How is fundamental mathematics efficiently evaluated by programming languages?

    - by Korvin Szanto
    As I get more and more involved with the theory behind programming, I find myself fascinated and dumbfounded by seemingly simple things.. I realize that my understanding of the majority of fundamental processes is justified through circular logic Q: How does this work? A: Because it does! I hate this realization! I love knowledge, and on top of that I love learning, which leads me to my question (albeit it's a broad one). Question: How are fundamental mathematical operators assessed with programming languages? How have current methods been improved? Example var = 5 * 5; My interpretation: $num1 = 5; $num2 = 5; $num3 = 0; while ($num2 > 0) { $num3 = $num3 + $num1; $num2 = $num2 - 1; } echo $num3; This seems to be highly inefficient. With Higher factors, this method is very slow while the standard built in method is instantanious. How would you simulate multiplication without iterating addition? var = 5 / 5; How is this even done? I can't think of a way to literally split it 5 into 5 equal parts. var = 5 ^ 5; Iterations of iterations of addition? My interpretation: $base = 5; $mod = 5; $num1 = $base; while ($mod > 1) { $num2 = 5; $num3 = 0; while ($num2 > 0) { $num3 = $num3 + $num1; $num2 = $num2 - 1; } $num1 = $num3; $mod -=1; } echo $num3; Again, this is EXTREMELY inefficient, yet I can't think of another way to do this. This same question extends to all mathematical related functions that are handled automagically.

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  • How can I get nVidia CUDA or OpenCL working on a laptop with nVidia discrete card/Intel Integrated Graphics?

    - by PeterDC
    Background: I'm a 3D artist (as a hobby) and have recently started using Ubuntu 12.04 LTS as a dual-boot with Windows 7. It's running on my a fairly new 64-bit Toshiba laptop with an nVidia GeForce GT 540M GPU (graphics card). It also, however has Intel Integrated Graphics (which I suspect Ubuntu's been using). So, when I render my 3D scenes to images on Windows, I am able to choose between using my CPU or my nVidia GPU (faster). From the 3D application, I can set the GPU to use either CUDA or OpenCL. In Ubuntu, there's no GPU option. After doing (too much?) research on the issues with Linux and the nVidia Optimus technology, I am slightly more enlightened, but a lot more confused. I don't care one bit about the Optimus technology, as battery life is not by any means an issue for me. Here's my question: What can I do to be able to use CUDA-utilizing programs (such as Blender) on my nVidia GPU in Ubuntu? Will I need nVidia drivers? (I have heard they don't play nicely with Optimus setups on Linux.) Is there at least a way to use OpenCL on my GPU in Ubuntu?

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  • Is it possible to plot a single density over a discrete variable?

    - by mattrepl
    The x-axis is time broken up into time intervals. There is an interval column in the data frame that specifies the time for each row. Plotting a histogram or line using geom_histogram and geom_freqpoly works great, but I'd like to use geom_density to get a filled area. Perhaps there is a better way to achieve this. Right now, if I use geom_density, curves are created for each discrete factor level instead of smoothing over all of them.

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