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  • System of linear equations in C++?

    - by Archagon
    I need to solve a system of linear equations in my program. Is there a simple linear algebra library for C++, preferably comprised of no more than a few headers? I've been looking for nearly an hour, and all the ones I found require messing around with Linux, compiling DLLs in MinGW, etc. etc. etc. (I'm using Visual Studio 2008.)

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  • Grapher: Edit Equations Without GUI

    - by Nathan G.
    I'm trying to edit the equation of a Grapher file without opening the Grapher UI. I've gotten as far as knowing that I need a hex editor to do this. I can't, however, find my equation in that file to change it. Does anyone know how Grapher stores this information, and how to change it? My ultimate goal is to be able to change the file through the shell so I can open it and have Grapher show me my new equation (that was set with the CL). Thanks! I will set a bounty if necessary.

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  • Algorithm to generate numerical concept hierarchy

    - by Christophe Herreman
    I have a couple of numerical datasets that I need to create a concept hierarchy for. For now, I have been doing this manually by observing the data (and a corresponding linechart). Based on my intuition, I created some acceptable hierarchies. This seems like a task that can be automated. Does anyone know if there is an algorithm to generate a concept hierarchy for numerical data? To give an example, I have the following dataset: Bangladesh 521 Brazil 8295 Burma 446 China 3259 Congo 2952 Egypt 2162 Ethiopia 333 France 46037 Germany 44729 India 1017 Indonesia 2239 Iran 4600 Italy 38996 Japan 38457 Mexico 10200 Nigeria 1401 Pakistan 1022 Philippines 1845 Russia 11807 South Africa 5685 Thailand 4116 Turkey 10479 UK 43734 US 47440 Vietnam 1042 for which I created the following hierarchy: LOWEST ( < 1000) LOW (1000 - 2500) MEDIUM (2501 - 7500) HIGH (7501 - 30000) HIGHEST ( 30000)

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  • silverlight for .NET / CLR based numerical computing on osx

    - by Jonathan Shore
    I'm interested in using F# for numerical work, but my platforms are not windows based. Mono still has a significant performance penalty for programs that generate a significant amount of short-lived objects (as would be typical for functional languages). Silverlight is available on OSX. I had seen some reference indicating that assemblies compiled in the usual way could not be referenced, but not clear on the details. I'm not interested in UIs, but wondering whether could use the VM bundled with silverlight effectively for execution? I would want to be able to reference a large library of numerical models I already have in java (cross-compiled via IKVM to .NET assemblies) and a new codebase written in F#. My hope would be that the silverlight VM on OSX has good performance and can reference external assemblies and native libraries. Is this doable?

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  • Function lfit in numerical recipes, providing a test function

    - by Simon Walker
    Hi I am trying to fit collected data to a polynomial equation and I found the lfit function from Numerical Recipes. I only have access to the second edition, so am using that. I have read about the lfit function and its parameters, one of which is a function pointer, given in the documentation as void (*funcs)(float, float [], int)) with the help The user supplies a routine funcs(x,afunc,ma) that returns the ma basis functions evaluated at x = x in the array afunc[1..ma]. I am struggling to understand how this lfit function works. An example function I found is given below: void fpoly(float x, float p[], int np) /*Fitting routine for a polynomial of degree np-1, with coe?cients in the array p[1..np].*/ { int j; p[1]=1.0; for (j=2;j<=np;j++) p[j]=p[j-1]*x; } When I run through the source code for the lfit function in gdb I can see no reference to the funcs pointer. When I try and fit a simple data set with the function, I get the following error message. Numerical Recipes run-time error... gaussj: Singular Matrix ...now exiting to system... Clearly somehow a matrix is getting defined with all zeroes. I am going to involve this function fitting in a large loop so using another language is not really an option. Hence why I am planning on using C/C++. For reference, the test program is given here: int main() { float x[5] = {0., 0., 1., 2., 3.}; float y[5] = {0., 0., 1.2, 3.9, 7.5}; float sig[5] = {1., 1., 1., 1., 1.}; int ndat = 4; int ma = 4; /* parameters in equation */ float a[5] = {1, 1, 1, 0.1, 1.5}; int ia[5] = {1, 1, 1, 1, 1}; float **covar = matrix(1, ma, 1, ma); float chisq = 0; lfit(x,y,sig,ndat,a,ia,ma,covar,&chisq,fpoly); printf("%f\n", chisq); free_matrix(covar, 1, ma, 1, ma); return 0; } Also confusing the issue, all the Numerical Recipes functions are 1 array-indexed so if anyone has corrections to my array declarations let me know also! Cheers

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  • Return numerical array in python

    - by khan
    Okay..this is kind of an interesting question. I have a php form through which user enters values for x and y like this: X: [1,3,4] Y: [2,4,5] These values are stored into database as varchars. From there, these are called by a python program which is supposed to use them as numerical (numpy) arrays. However, these are called as plain strings, which means that calculation can not be performed over them. Is there a way to convert them into numerical arrays before processing or is there something else which is wrong? Helpp!!

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  • assigning in system of differential equations

    - by Alireza
    hi every one! when i solve numerically a system of two differential equations: s1:=diff(nDi, t)=...; s2:=diff(nT, t)=...; ics:={...}; #initial condition. sys := {s1, s2, ics}: sol:=dsolve(sys,numeric); with respect to "t",then the solution (for example)for "t=4" is of the form, sol(4): [t=4, n1(t)=const1, n2(t)=const2]. now, how is possible to use values of n1(t) and n2(t) for all "t"'s in another equation, namely "p", which involved n1(t) or n2(t)(like: {p=a+n1(t)*n2(t)+f(t)},where "a" and "f(t)" are defined), and to plot "p" for an interval of "t"?

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  • Orbital equations, and power required to run them

    - by Adam Davis
    Due to a discussion on the SO IRC today, I'm curious about orbital mechanics, and The equations needed to solve orbital problems The computing power required to solve complex problems The question in particular is calculating when the Earth will plow into the Sun (or vice versa, depending on the frame of reference). I suspect that all the gravitational pulls within our solar system may need to be calculated, which makes me wonder what type of computer cluster is required, or can this be done on a single box? I don't have the experience to do a back of the napkin test here, but perhaps you do? Also, much thx to Gortok for the original inspiration (see comments).

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  • array_splice() - Numerical Offsets of Associative Arrays

    - by Alix Axel
    I'm trying to do something but I can't find any solution, I'm also having some trouble putting it into works so here is a sample code, maybe it'll be enough to demonstrate what I'm aiming for: $input = array ( 'who' => 'me', 'what' => 'car', 'more' => 'car', 'when' => 'today', ); Now, I want to use array_splice() to remove (and return) one element from the array: $spliced = key(array_splice($input, 2, 1)); // I'm only interested in the key... The above will remove and return 1 element (third argument) from $input (first argument), at offset 2 (second argument), so $spliced will hold the value more. I'll be iterating over $input with a foreach loop, I know the key to be spliced but the problem is I don't know its numerical offset and since array_splice only accepts integers I don't know what to do. A very dull example: $result = array(); foreach ($input as $key => $value) { if ($key == 'more') { // Remove the index "more" from $input and add it to $result. $result[] = key(array_splice($input, 2 /* How do I know its 2? */, 1)); } } I first though of using array_search() but it's pointless since it'll return the associative index.... How do I determine the numerical offset of a associative index?

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  • Reversible numerical calculations in Prolog

    - by user8472
    While reading SICP I came across logic programming chapter 4.4. Then I started looking into the Prolog programming language and tried to understand some simple assignments in Prolog. I found that Prolog seems to have troubles with numerical calculations. Here is the computation of a factorial in standard Prolog: f(0, 1). f(A, B) :- A > 0, C is A-1, f(C, D), B is A*D. The issues I find is that I need to introduce two auxiliary variables (C and D), a new syntax (is) and that the problem is non-reversible (i.e., f(5,X) works as expected, but f(X,120) does not). Naively, I expect that at the very least C is A-1, f(C, D) above may be replaced by f(A-1,D), but even that does not work. My question is: Why do I need to do this extra "stuff" in numerical calculations but not in other queries? I do understand (and SICP is quite clear about it) that in general information on "what to do" is insufficient to answer the question of "how to do it". So the declarative knowledge in (at least some) math problems is insufficient to actually solve these problems. But that begs the next question: How does this extra "stuff" in Prolog help me to restrict the formulation to just those problems where "what to do" is sufficient to answer "how to do it"?

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  • Numerical calculations in Prolog

    - by user8472
    While reading SICP I came across logic programming chapter 4.4. Then I started looking into the Prolog programming language and tried to understand some simple assignments in Prolog. I found that Prolog seems to have troubles with numerical calculations. Here is the computation of a factorial in standard Prolog: f(0, 1). f(A, B) :- A > 0, C is A-1, f(C, D), B is A*D. The issues I find is that I need to introduce two auxiliary variables (C and D), a new syntax (is) and that the problem is non-reversible (i.e., f(5,X) works as expected, but f(X,120) does not). Naively, I expect that at the very least C is A-1, f(C, D) above may be replaced by f(A-1,D), but even that does not work. My question is: Why do I need to do this extra "stuff" in numerical calculations but not in other queries? I do understand (and SICP is quite clear about it) that in general information on "what to do" is insufficient to answer the question of "how to do it". So the declarative knowledge in (at least some) math problems is insufficient to actually solve these problems. But that begs the next question: How does this extra "stuff" in Prolog help me to restrict the formulation to just those problems where "what to do" is sufficient to answer "how to do it"?

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  • Solving for the coefficent of linear equations with one known coefficent

    - by CppLearner
    clc; clear all; syms y a2 a3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % [ 0.5 0.25 0.125 ] [ a2 ] [ y ] % [ 1 1 1 ] [ a3 ] = [ 3 ] % [ 2 4 8 ] [ 6 ] [ 2 ] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% M = [0.5 0.25 0.125; 1 1 1; 2 4 8]; t = [a2 a3 6]; r = [y 3 2]; sol = M * t' s1 = solve(sol(1), a2) % solve for a2 s2 = solve(sol(2), a3) % solve for a3 This is what I have so far. These are my output sol = conj(a2)/2 + conj(a3)/4 + 3/4 conj(a2) + conj(a3) + 6 2*conj(a2) + 4*conj(a3) + 48 s1 = - conj(a3)/2 - 3/2 - Im(a3)*i s2 = - conj(a2) - 6 - 2*Im(a2)*i sol looks like what we would have if we put them back into equation form: 0.5 * a2 + 0.25 * a3 + 0.125 * a4 a2 + a3 + a4 = 3 2*a2 + 4*a3 + 8*a4 = 2 where a4 is known == 6. My problem is, I am stuck with how to use solve to actually solve these equations to get the values of a2 and a3. s2 solve for a3 but it doesn't match what we have on paper (not quite). a2 + a3 + 6 = 3 should yield a3 = -3 - a2. because of the imaginary. Somehow I need to equate the vector solution sol to the values [y 3 2] for each row.

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  • Large sparse (stiff) ODE system needed for testing

    - by macydanim
    I hope this is the right place for this question. I have been working on a sparse stiff implicit ODE solver and have finished the code so far. I now tested the solver with the Van der Pol equation, and another stiff problem, which is of dimension 4. But to perform better tests I am searching for a bigger system. I'm thinking of the order N = 100...1000, if possible stiff and sparse. Does anybody have an example I could use? I really don't know where to search.

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  • How is this number calculated?

    - by Hamid
    I have numbers; A == 0x20000000 B == 18 C == (B/10) D == 0x20000004 == (A + C) A and D are in hex, but I'm not sure what the assumed numeric bases of the others are (although I'd assume base 10 since they don't explicitly state a base. It may or may not be relevant but I'm dealing with memory addresses, A and D are pointers. The part I'm failing to understand is how 18/10 gives me 0x4. Edit: Code for clarity: *address1 (pointer is to address: 0x20000000) printf("Test1: %p\n", address1); printf("Test2: %p\n", address1+(18/10)); printf("Test3: %p\n", address1+(21/10)); Output: Test1: 0x20000000 Test2: 0x20000004 Test3: 0x20000008

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  • Equation solver project

    - by Victor Barbu
    I would like to start a project destinated to students. My application has to solve any kind of equation, passed by the user as a string, exactly like in Matlab solve function. How shluld I do this? What programming language is the best for this purpose? Thanks in advance. P.S This is a screenshot made in Matlab. This is how I would like the user to insert and receive the answer: Another example:

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  • How do I assign a number value to a non-numerical value in Excel

    - by Keyslinger
    Greetings I have an some survey responses with values like "VU" for "Very Unlikely" and "S" for Sometimes. Each survey response occupies a cell. For each cell containing a survey response, I want to fill another cell with a corresponding number. For example, for every cell containing "VU" I want to fill a corresponding cell with the number 1. How is this done?

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  • Excel Pivot Tables -- Divide Numerical Column Data into Ranges

    - by ktm5124
    Hi, I have an Excel spreadsheet with a column called "Time Elapsed" that stores the number of days it took to complete a task. I would like to make a pivot table out of this spreadsheet where I divide the "Time Elapsed" column into ranges, e.g., how many tasks took 0 to 4 days to complete how many tasks took 5 to 9 days how many took 10 to 14 days how many took 15+ days Do I have to create new columns in my spreadsheet dedicated to each interval (0 to 4, 5 to 9, etc.) or can I use some feature of pivot tables to separate my one "Time Elapsed" column into intervals? Thanks in advance.

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  • Access element in json having numerical index

    - by hunt
    i have following format of json in which i want to asscess 0.4 , kem , 2 , 2000 values but it seems it doesn't have name index so how one can access it in jquery. when i paste following code in json viewer then i am getting numerical index for 0.4 , kem , 2 "td": [ { "@attributes": { "class": "odd" }, "span": [ "3", "7" ] }, "0.4", "Kem", "24\/04\/2010", "2000", "2", "14000", "Good", "Buckley", "56.0", "2:05.32", "36.65", "54.5" ] }

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  • Java code optimization leads to numerical inaccuracies and errors

    - by rano
    I'm trying to implement a version of the Fuzzy C-Means algorithm in Java and I'm trying to do some optimization by computing just once everything that can be computed just once. This is an iterative algorithm and regarding the updating of a matrix, the clusters x pixels membership matrix U, this is the update rule I want to optimize: where the x are the element of a matrix X (pixels x features) and v belongs to the matrix V (clusters x features). And m is a parameter that ranges from 1.1 to infinity. The distance used is the euclidean norm. If I had to implement this formula in a banal way I'd do: for(int i = 0; i < X.length; i++) { int count = 0; for(int j = 0; j < V.length; j++) { double num = D[i][j]; double sumTerms = 0; for(int k = 0; k < V.length; k++) { double thisDistance = D[i][k]; sumTerms += Math.pow(num / thisDistance, (1.0 / (m - 1.0))); } U[i][j] = (float) (1f / sumTerms); } } In this way some optimization is already done, I precomputed all the possible squared distances between X and V and stored them in a matrix D but that is not enough, since I'm cycling througn the elements of V two times resulting in two nested loops. Looking at the formula the numerator of the fraction is independent of the sum so I can compute numerator and denominator independently and the denominator can be computed just once for each pixel. So I came to a solution like this: int nClusters = V.length; double exp = (1.0 / (m - 1.0)); for(int i = 0; i < X.length; i++) { int count = 0; for(int j = 0; j < nClusters; j++) { double distance = D[i][j]; double denominator = D[i][nClusters]; double numerator = Math.pow(distance, exp); U[i][j] = (float) (1f / (numerator * denominator)); } } Where I precomputed the denominator into an additional column of the matrix D while I was computing the distances: for (int i = 0; i < X.length; i++) { for (int j = 0; j < V.length; j++) { double sum = 0; for (int k = 0; k < nDims; k++) { final double d = X[i][k] - V[j][k]; sum += d * d; } D[i][j] = sum; D[i][B.length] += Math.pow(1 / D[i][j], exp); } } By doing so I encounter numerical differences between the 'banal' computation and the second one that leads to different numerical value in U (not in the first iterates but soon enough). I guess that the problem is that exponentiate very small numbers to high values (the elements of U can range from 0.0 to 1.0 and exp , for m = 1.1, is 10) leads to ver y small values, whereas by dividing the numerator and the denominator and THEN exponentiating the result seems to be better numerically. The problem is it involves much more operations. Am I doing something wrong? Is there a possible solution to get both the code optimized and numerically stable? Any suggestion or criticism will be appreciated.

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  • Math/numerical formula every computer programmer should know

    - by aaa
    This is a follow-up question to What should every programmer know and Is mathematics necessary. So the question is, as a computer programmer, what is the most important/useful mathematical or numerical formula that you use? By Formula I mean anything that involves less obvious manipulations, whenever binomial coefficients or bit hacks. I work with multidimensional arrays and various matrix representations. So for me most commonly used formulas are: A(i,j,k,..) = a[i + j*Dim0 + k*Dim0*Dim1 + ... to map indexes to one dimension ( which is basic address calculation which many people do not seem to know). And triangular number T(i) = (i*i + i)/2 which is related to binomial coefficients, used to calculate address in triangular matrixes and many other things. What is your workhorse formula that you think programmer should know?

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