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  • GCD function in matlab

    - by SalemFayad
    hi, i am looking for a way to implement the "gcd" function used in matlab in another language but i really cant understand the way it functions. it says in http://www.mathworks.com/access/helpdesk/help/techdoc/ref/gcd.html that: "[G,C,D] = gcd(A,B) returns both the greatest common divisor array G, and the arrays C and D, which satisfy the equation: A(i).*C(i) + B(i).*D(i) = G(i)." but it says nothing about how it calculates C and D. i would be grateful if someone has a clearer idea about this subject! thanks:)

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  • Number Algorithm

    - by James
    I've been struggling to wrap my head around this for some reason. I have 15 bits that represent a number. The bits must match a pattern. The pattern is defined in the way the bits start out: they are in the most flush-right representation of that pattern. So say the pattern is 1 4 1. The bits will be: 000000010111101 So the general rule is, take each number in the pattern, create that many bits (1, 4 or 1 in this case) and then have at least one space separating them. So if it's 1 2 6 1 (it will be random): 001011011111101 Starting with the flush-right version, I want to generate every single possible number that meets that pattern. The # of bits will be stored in a variable. So for a simple case, assume it's 5 bits and the initial bit pattern is: 00101. I want to generate: 00101 01001 01010 10001 10010 10100 I'm trying to do this in Objective-C, but anything resembling C would be fine. I just can't seem to come up with a good recursive algorithm for this. It makes sense in the above example, but when I start getting into 12431 and having to keep track of everything it breaks down.

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  • Mathematics for Computer Science Students

    - by Ender
    To cut a long story short, I am a CS student that has received no formal Post-16 Maths education for years. Right now even my Algebra is extremely rusty and I have a couple of months to shape up my skills. I've got a couple of video lectures in my bookmarks, consisting of: Pre-Calculus Algebra Calculus Probability Introduction to Statistics Differential Equations Linear Algebra My aim as of today is to be able to read the CLRS book Introduction to Algorithms and be able to follow the Mathematical notation in that, as well as being able to confidently read and back-up any arguments written in Mathematical notation. Aside from these video lectures, can anyone recommend any good books to help teach someone wishing to go from a low-foundation level to a more advanced level of Mathematics? Just as a note, I've taken a first-year module in Analytical Modelling, so I understand some of the basic concepts of Discrete Mathematics. EDIT: Just a note to those that are looking to learn Linear Algebra using the Video Lectures I have posted up. Peteris Krumins' Blog contains a run-through of these lecture notes as well as his own commentary and lecture notes, an invaluable resource for those looking to follow the lectures too.

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  • What's the best way to normalize scores for ranking things?

    - by beagleguy
    hi all, I'm curious how to do normalizing of numbers for a ranking algorithm let's say I want to rank a link based on importance and I have two columns to work with so a table would look like url | comments | views now I want to rank comments higher than views so I would first think to do comments*3 or something to weight it, however if there is a large view number like 40,000 and only 4 comments then the comments weight gets dropped out. So I'm thinking I have to normalize those scores down to a more equal playing field before I can weight them. Any ideas or pointers to how that's usually done? thanks

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  • Simple 3x3 matrix inverse code (C++)

    - by batty
    What's the easiest way to compute a 3x3 matrix inverse? I'm just looking for a short code snippet that'll do the trick for non-singular matrices, possibly using Cramer's rule. It doesn't need to be highly optimized. I'd prefer simplicity over speed. I'd rather not link in additional libraries. Primarily I was hoping to have this on Stack Overflow so that I wouldn't have to hunt around for it or rewrite from scratch again next time.

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  • Rot13 for numbers.

    - by dreeves
    EDIT: Now a Major Motion Blog Post at http://messymatters.com/sealedbids The idea of rot13 is to obscure text, for example to prevent spoilers. It's not meant to be cryptographically secure but to simply make sure that only people who are sure they want to read it will read it. I'd like to do something similar for numbers, for an application involving sealed bids. Roughly I want to send someone my number and trust them to pick their own number, uninfluenced by mine, but then they should be able to reveal mine (purely client-side) when they're ready. They should not require further input from me or any third party. (Added: Note the assumption that the recipient is being trusted not to cheat.) It's not as simple as rot13 because certain numbers, like 1 and 2, will recur often enough that you might remember that, say, 34.2 is really 1. Here's what I'm looking for specifically: A function seal() that maps a real number to a real number (or a string). It should not be deterministic -- seal(7) should not map to the same thing every time. But the corresponding function unseal() should be deterministic -- unseal(seal(x)) should equal x for all x. I don't want seal or unseal to call any webservices or even get the system time (because I don't want to assume synchronized clocks). (Added: It's fine to assume that all bids will be less than some maximum, known to everyone, say a million.) Sanity check: > seal(7) 482.2382 # some random-seeming number or string. > seal(7) 71.9217 # a completely different random-seeming number or string. > unseal(seal(7)) 7 # we always recover the original number by unsealing.

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  • Zip Code Radius Search question...

    - by KnockKnockWhosThere
    I'm wondering if it's possible to find all points by longitude and latitude within X radius of one point? So, if I provide a latitude/longitude of -76.0000, 38.0000, is it possible to simply find all the possible coordinates within (for example) a 10 mile radius of that? I know that there's a way to calculate the distance between two points, which is why I'm not clear as to whether this is possible... Because, it seems like you need to know the center coordinates (-76 and 38 in this case) as well as the coordinates of every other point in order to determine whether it falls within the specified radius... Is that right?

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  • NSDecimalNumber subtraction

    - by happyCoding25
    Hello, I need to subtract 0.5 from number a and set the answer to number b. My code looks like it would work but I'm not sure what I'm doing wrong. The error I get Is on the subtraction line, the error says incompatible type for argument 1 of 'decimalNumberBySubtracting:'. Heres my header: (Note: I only showed the numbers because the header is large) NSDecimalNumber *a; NSDecimalNumber *b; Heres the rest: (Assume this is in an IBAction) b = [a decimalNumberBySubtracting:0.5]; If anyone knows how to properly subtract any help would be appreciated.

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  • How to generate a lower frequency version of a signal in Matlab?

    - by estourodepilha.com
    With a sine input, I tried to modify it's frequency cutting some lower frequencies in the spectrum, shifting the main frequency towards zero. As the signal is not fftshifted I tried to do that by eliminating some samples at the begin and at the end of the fft vector: interval = 1; samplingFrequency = 44100; signalFrequency = 440; sampleDuration = 1 / samplingFrequency; timespan = 1 : sampleDuration : (1 + interval); original = sin(2 * pi * signalFrequency * timespan); fourierTransform = fft(original); frequencyCut = 10; %% Hertz frequencyCut = floor(frequencyCut * (length(pattern) / samplingFrequency) / 4); %% Samples maxFrequency = length(fourierTransform) - (2 * frequencyCut); signal = ifft(fourierTransform(frequencyCut + 1:maxFrequency), 'symmetric'); But it didn't work as expected. I also tried to remove the center part of the spectrum, but it wielded a higher frequency sine wave too. How to make it right?

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  • How to perform spatial partitioning in n-dimensions?

    - by kevin42
    I'm trying to design an implementation of Vector Quantization as a c++ template class that can handle different types and dimensions of vectors (e.g. 16 dimension vectors of bytes, or 4d vectors of doubles, etc). I've been reading up on the algorithms, and I understand most of it: here and here I want to implement the Linde-Buzo-Gray (LBG) Algorithm, but I'm having difficulty figuring out the general algorithm for partitioning the clusters. I think I need to define a plane (hyperplane?) that splits the vectors in a cluster so there is an equal number on each side of the plane. [edit to add more info] This is an iterative process, but I think I start by finding the centroid of all the vectors, then use that centroid to define the splitting plane, get the centroid of each of the sides of the plane, continuing until I have the number of clusters needed for the VQ algorithm (iterating to optimize for less distortion along the way). The animation in the first link above shows it nicely. My questions are: What is an algorithm to find the plane once I have the centroid? How can I test a vector to see if it is on either side of that plane?

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  • Is there a Java library with 3D spline functions?

    - by Liam
    In particular, I need a way to represent a curve/spline that passes through a set of known 3D points, and a way of finding other points on the curve/spline, by subdivision/interpolation. For example, if I have a set of points P0 to PN, I want to find 100 points between P0 and P1 that are on a spline that passes through P0 and P1. I see that Java3D's KBRotPosScaleSplinePathInterpolator performs such a calculation, but it is tied to that API's scenegraph model and I do not see how to return the values I need.

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  • Draw Lines Over a Circle

    - by VOX
    There's a line A-B and C at the center between A and B. It forms a circle as in the figure. If we assume A-B line as a diameter of the circle and then C is it's center. My problem is I have no idea how to draw another three lines (in blue) each 45 degree away from AC or AB. No, this is not a homework, it's part of my complex geometry in a rendering. http://www.freeimagehosting.net/image.php?befcd84d8c.png

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  • Runge-Kutta Method with adaptive step

    - by infoholic_anonymous
    I am implementing Runge-Kutta method with adaptive step in matlab. I get different results as compared to matlab's own ode45 and my own implementation of Runge-Kutta method with fixed step. What am I doing wrong in my code? Is it possible? function [ result ] = rk4_modh( f, int, init, h, h_min ) % % f - function handle % int - interval - pair (x_min, x_max) % init - initial conditions - pair (y1(0),y2(0)) % h_min - lower limit for h (step length) % h - initial step length % x - independent variable ( for example time ) % y - dependent variable - vertical vector - in our case ( y1, y2 ) function [ k1, k2, k3, k4, ka, y ] = iteration( f, h, x, y ) % core functionality performed within loop k1 = h * f(x,y); k2 = h * f(x+h/2, y+k1/2); k3 = h * f(x+h/2, y+k2/2); k4 = h * f(x+h, y+k3); ka = (k1 + 2*k2 + 2*k3 + k4)/6; y = y + ka; end % constants % relative error eW = 1e-10; % absolute error eB = 1e-10; s = 0.9; b = 5; % initialization i = 1; x = int(1); y = init; while true hy = y; hx = x; %algorithm [ k1, k2, k3, k4, ka, y ] = iteration( f, h, x, y ); % error estimation for j=1:2 [ hk1, hk2, hk3, hk4, hka, hy ] = iteration( f, h/2, hx, hy ); hx = hx + h/2; end err(:,i) = abs(hy - y); % step adjustment e = abs( hy ) * eW + eB; a = min( e ./ err(:,i) )^(0.2); mul = a * s; if mul >= 1 % step length admitted keepH(i) = h; k(:,:,i) = [ k1, k2, k3, k4, ka ]; previous(i,:) = [ x+h, y' ]; %' i = i + 1; if floor( x + h + eB ) == int(2) break; else h = min( [mul*h, b*h, int(2)-x] ); x = x + keepH(i-1); end else % step length requires further adjustments h = mul * h; if ( h < h_min ) error('Computation with given precision impossible'); end end end result = struct( 'val', previous, 'k', k, 'err', err, 'h', keepH ); end The function in question is: function [ res ] = fun( x, y ) % res(1) = y(2) + y(1) * ( 0.9 - y(1)^2 - y(2)^2 ); res(2) = -y(1) + y(2) * ( 0.9 - y(1)^2 - y(2)^2 ); res = res'; %' end The call is: res = rk4( @fun, [0,20], [0.001; 0.001], 0.008 ); The resulting plot for x1 : The result of ode45( @fun, [0, 20], [0.001, 0.001] ) is:

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  • Using bitwise operators on > 32 bit integers

    - by dqhendricks
    I am using bitwise operations in order to represent many access control flags within one integer. ADMIN_ACCESS = 1; EDIT_ACCOUNT_ACCESS = 2; EDIT_ORDER_ACCESS = 4; var myAccess = 3; // ie: ( ADMIN_ACCESS | EDIT_ACCOUNT_ACCESS ) if ( myAccess & EDIT_ACCOUNT_ACCESS ) { // check for correct access // allow for editing of account } Most of this is occurring on the PHP side of my project. There is one piece however where Javascript is used to join several access flags using | when saving someone's access level. This works fine to a point. I have found that once an integer (flag) gets too large ( 32bit), it no longer works correctly with bitwise operators in Javascript. For instance: alert( 4294967296 | 1 ); // equals 1, but should equal 4294967297 I am trying to find a workaround for this so that I do not have to limit my number of access control flags to 32. Each access control flag is two times the previous control flag so that each control flag will not interfere with other control flags. dec(4) = bin(100) dec(8) = bin(1000) dec(16) = bin(10000) I have noticed that when adding two of these flags together with a simple +, it seems to come out with the same answer as a bitwise or operation, but am having trouble wrapping my head around whether this is a simple substitution, or if there might be problems with doing this. Can anyone comment on the validity of this workaround? Example: (4294967296 | 262144 | 524288) == (4294967296 + 262144 + 524288)

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  • solving origin of a vectors

    - by Mike
    I have two endpoints (xa,ya) and (xb,yb) of two vectors, respectively a and b, originating from a same point (xo, yo). Also, I know that |a|=|b|+s, where s is a constant. I tried to compute the origin (xo, yo) but seem to fail at some point. How to solve this?

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  • Finding coordinates of a point between two points?

    - by Nicros
    Doing some 3D stuff in wpf- want to use a simpler test to see if everything is working (before moving to curves). The basic question is given two points x1,y1,z1 and x2,y2,z2 I have calculated the distance between the points. But how to find the coordinates of another point (x3,y3,z3) that lies on that line at some distance? I.e. if my line is 100 long between -50,0,0 and 50,0,0 what are the coordinates of the point at 100 * 0.1 along the line? I think this is a simple formula but I haven't found it yet....

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  • How to solve such system with given parts of it? (maple)

    - by Kabumbus
    So I had a system #for given koefs k:=3; n:=3; #let us solve system: koefSolution:= solve({ sum(a[i], i = 0 .. k) = 0, sum(a[i], i = 0 .. k)-(sum(b[i], i = 0 .. k)) = 0, sum(i^n*a[i], i = 0 .. k)-(sum(i^(n-1)*b[i], i = 0 .. k)) = 0 }); So I have a vector like koefSolution := { a[0] = 7*a[2]+26*a[3]-b[1]-4*b[2]-9*b[3], a[1] = -8*a[2]-27*a[3]+b[1]+4*b[2]+9*b[3], a[2] = a[2], a[3] = a[3], b[0] = -b[1]-b[2]-b[3], b[1] = b[1], b[2] = b[2], b[3] = b[3]} I have a[0] so I try solve({koefSolution, a[0] = 1}); why it does not solve my system for given a[0]? ( main point here is to fill koefSolution with given a[] and b[] and optimize.)

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  • bash: expanding variables with spaces

    - by adam n
    i have a file called physics 1b.sh in bash, if i try x="physics 1b" grep "string" "$x".sh grep complains: grep: physics 1b: No such file or directory. However, when i do grep "string" physics\ 1b.sh it works fine. So i guess the problem is something to do with the variable not being expanded to include the backslash that grep needs to recognize the space. How do i get this to work? using bash 3.2, mac os 10.6.

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  • Power Law distribution for a given exponent in C# using MathNet

    - by Eric Tobias
    Hello! I am currently working on a project where I need to generate multiple values (floats or doubles preferably) that follow a power law distribution with a given exponent! I was advised to use the MathNet.Iridium library to help me. The problem I have is that the documentation is not as explicit as it should be if there is any! I see multiple distributions that fit the general idea of the power law distribution but I cannot pinpoint a good distribution to use with a certain exponent as a parameter. Does anybody have more experience in that matter and could give me some hints or advice?

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