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  • Matlab code help. Backward Euler method.

    - by m0s
    Here is the matlab/freemat code I got to solve ODE numerically using backward Euler method. However the results are inconsistent with my textbook results, and sometimes even ridiculously inconsistent. Please point out what is wrong with the code. I have already asked this question on mathoverflow.com no help there, hope someone here can help. function [x,y]=backEuler(f,xinit,yinit,xfinal,h) %f - this is your y prime %xinit - initial X %yinit - initial Y %xfinal - final X %h - step size n=(xfinal-xinit)/h; %Calculate steps %Inititialize arrays... %1st elements take xinit and yinit corespondigly, the rest fill with 0s x=[xinit zeros(1,n)]; y=[yinit zeros(1,n)]; %Numeric routine for i=1:n x(i+1)=x(i)+h; ynew=y(i)+h*(f(x(i),y(i))); y(i+1)=y(i)+h*f(x(i+1),ynew); end end

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  • SVD factorization

    - by Simon
    How can i use the bidiagonal and diagonal form to compute the SVD factorization. I think my real problem is that i don't understand this concepts.

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  • Efficiently solving sparse matrices

    - by anon
    For solving spare matrices, in general, how big does the matrix have to be (as a rule of thumb) for methods like congraduate descent to be faster than brute force solvers (that do not take advantage o sparsity)?

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  • Implementation of GNU Scientific Library?

    - by anon
    Does anyone know a collection of articles or books that describes the implementation of the GNU Scientific Library? This question is not about using the GSL; it's about how the GSL is implemented, their design decisions / tradeoffs. Thanks!

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  • incremental way of counting quantiles for large set of data

    - by Gacek
    I need to count the quantiles for a large set of data. Let's assume we can get the data only through some portions (i.e. one row of a large matrix). To count the Q3 quantile one need to get all the portions of the data and store it somewhere, then sort it and count the quantile: List<double> allData = new List<double>(); foreach(var row in matrix) // this is only example. In fact the portions of data are not rows of some matrix { allData.AddRange(row); } allData.Sort(); double p = 0.75*allData.Count; int idQ3 = (int)Math.Ceiling(p) - 1; double Q3 = allData[idQ3]; Now, I would like to find a way of counting this without storing the data in some separate variable. The best solution would be to count some parameters od mid-results for first row and then adjust it step by step for next rows. Note: These datasets are really big (ca 5000 elements in each row) The Q3 can be estimated, it doesn't have to be an exact value. I call the portions of data "rows", but they can have different leghts! Usually it varies not so much (+/- few hundred samples) but it varies! This question is similar to this one: http://stackoverflow.com/questions/1058813/on-line-iterator-algorithms-for-estimating-statistical-median-mode-skewness But I need to count quantiles. ALso there are few articles in this topic, i.e.: http://web.cs.wpi.edu/~hofri/medsel.pdf http://portal.acm.org/citation.cfm?id=347195&dl But before I would try to implement these, I wanted to ask you if there are maybe any other, qucker ways of counting the 0.25/0.75 quantiles?

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  • File Segmentation when trying to write in a file

    - by user1286390
    I am trying in C language to use the method of bisection to find the roots of some equation, however when I try to write every step of this process in a file I get the problem "Segmentation fault". This might be an idiot fault that I did, however I have been trying to solve this for a long time. I am compiling using gcc and that is the code: #include <stdio.h> #include <stdlib.h> #include <math.h> #define R 1.0 #define h 1.0 double function(double a); void attractor(double *a1, double *a2, double *epsilon); void attractor(double *a1, double *a2, double *epsilon) { FILE* bisection; double a2_copia, a3, fa1, fa2; bisection = fopen("bisection-part1.txt", "w"); fa1 = function(*a1); fa2 = function(*a2); if(function(*a1) - function(*a2) > 0.0) *epsilon = function(*a1) - function(*a2); else *epsilon = function(*a2) - function(*a1); fprintf(bisection, "a1 a2 fa1 fa2 epsilon\n"); a2_copia = 0.0; if(function(*a1) * function(*a2) < 0.0 && *epsilon >= 0.00001) { a3 = *a2 - (*a2 - *a1); a2_copia = *a2; *a2 = a3; if(function(*a1) - function(*a2) > 0.0) *epsilon = function(*a1) - function(*a2); else *epsilon = function(*a2) - function(*a1); if(function(*a1) * function(*a2) < 0.0 && *epsilon >= 0.00001) { fprintf(bisection, "%.4f %.4f %.4f %.4f %.4f\n", *a1, *a2, function(*a1), function(*a1), *epsilon); attractor(a1, a2, epsilon); } else { *a2 = a2_copia; *a1 = a3; if(function(*a1) - function(*a2) > 0) *epsilon = function(*a1) - function(*a2); else *epsilon = function(*a2) - function(*a1); if(function(*a1) * function(*a2) < 0.0 && *epsilon >= 0.00001) { fprintf(bisection, "%.4f %.4f %.4f %.4f %.4f\n", *a1, *a2, function(*a1), function(*a1), *epsilon); attractor(a1, a2, epsilon); } } } fa1 = function(*a1); fa2 = function(*a2); if(function(*a1) - function(*a2) > 0.0) *epsilon = function(*a1) - function(*a2); else *epsilon = function(*a2) - function(*a1); fprintf(bisection, "%.4f %.4f %.4f %.4f %.4f\n", a1, a2, fa1, fa2, epsilon); } double function(double a) { double fa; fa = (a * cosh(h / (2 * a))) - R; return fa; } int main() { double a1, a2, fa1, fa2, epsilon; a1 = 0.1; a2 = 0.5; fa1 = function(a1); fa2 = function(a2); if(fa1 - fa2 > 0.0) epsilon = fa1 - fa2; else epsilon = fa2 - fa1; if(epsilon >= 0.00001) { fa1 = function(a1); fa2 = function(a2); attractor(&a1, &a2, &epsilon); fa1 = function(a1); fa2 = function(a2); if(fa1 - fa2 > 0.0) epsilon = fa1 - fa2; else epsilon = fa2 - fa1; } if(epsilon < 0.0001) printf("Vanish at %f", a2); else printf("ERROR"); return 0; } Thanks anyway and sorry if this question is not suitable.

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  • troubles with integration on matlab

    - by user648666
    I'd like some help please I really need to solve this problem. Well before anything thank you for your time... My problem: I have a matrix (826x826 double) and I want to integrate this matrix with respect to a vector of (826x1 double) I don't have the functions of any of this. Is there a command or an algorithm to take the integral of a matrix with respect to a vector? Please I really need help, I'm such a newbie at matlab. Sincerely. George

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  • What's a good way to add a large number of small floats together?

    - by splicer
    Say you have 100000000 32-bit floating point values in an array, and each of these floats has a value between 0.0 and 1.0. If you tried to sum them all up like this result = 0.0; for (i = 0; i < 100000000; i++) { result += array[i]; } you'd run into problems as result gets much larger than 1.0. So what are some of the ways to more accurately perform the summation?

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  • How can I add floats together in different orders, and always get the same total?

    - by splicer
    Let's say I have three 32-bit floating point values, a, b, and c, such that (a + b) + c != a + (b + c). Is there summation algorithm, perhaps similar to Kahan summation, that guarantees that these values can be summed in any order and always arrive at the exact same (fairly accurate) total? I'm looking for the general case (i.e. not a solution that only deals with 3 numbers). Is arbitrary precision arithmetic the only way to go? I'm dealing with very large data sets, so I'd like to avoid the overhead of using arbitrary precision arithmetic if possible. Thanks!

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  • PHP: Is_numeric returns false on 0

    - by Industrial
    Hi everyone, Is_numeric() as well as is_int() returns false if the value is 0. What can i do instead to verify that a specific value is numbers only in PHP? Are we heading straight for the Regular Expressions camp, or are there some nice, handy feature for this out there already? Thanks!

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  • Outer product using CBLAS

    - by The Dude
    I am having trouble utilizing CBLAS to perform an Outer Product. My code is as follows: //===SET UP===// double x1[] = {1,2,3,4}; double x2[] = {1,2,3}; int dx1 = 4; int dx2 = 3; double X[dx1 * dx2]; for (int i = 0; i < (dx1*dx2); i++) {X[i] = 0.0;} //===DO THE OUTER PRODUCT===// cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans, dx1, dx2, 1, 1.0, x1, dx1, x2, 1, 0.0, X, dx1); //===PRINT THE RESULTS===// printf("\nMatrix X (%d x %d) = x1 (*) x2 is:\n", dx1, dx2); for (i=0; i<4; i++) { for (j=0; j<3; j++) { printf ("%lf ", X[j+i*3]); } printf ("\n"); } I get: Matrix X (4 x 3) = x1 (*) x2 is: 1.000000 2.000000 3.000000 0.000000 -1.000000 -2.000000 -3.000000 0.000000 7.000000 14.000000 21.000000 0.000000 But the correct answer is found here: https://www.sharcnet.ca/help/index.php/BLAS_and_CBLAS_Usage_and_Examples I have seen: Efficient computation of kronecker products in C But, it doesn't help me because they don't actually say how to utilize dgemm to actually do this... Any help? What am I doing wrong here?

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  • Netlogo programming question - is it possible to put balanced chemical equations in a model?

    - by user286190
    hi I was wondering if it was possible to put balanced chemical equations, and if possible including state symbols, in the existing netlogo model that i am using, i havenot seen any examples in the models library so was not sure if it was possible. I wanted the model to be able to allow the user to input a balanced chemical equilibrium equation, or the model displays the the equation so then the user can select from them if they do not want to enter their own any help will be greatly appreciated thanks for example ethane + oxygen -- carbon dioxide + steam C2H6 + O2 -- CO2 + H2O

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  • difference equations in MATLAB - why the need to switch signs?

    - by jefflovejapan
    Perhaps this is more of a math question than a MATLAB one, not really sure. I'm using MATLAB to compute an economic model - the New Hybrid ISLM model - and there's a confusing step where the author switches the sign of the solution. First, the author declares symbolic variables and sets up a system of difference equations. Note that the suffixes "a" and "2t" both mean "time t+1", "2a" means "time t+2" and "t" means "time t": %% --------------------------[2] MODEL proc-----------------------------%% % Define endogenous vars ('a' denotes t+1 values) syms y2a pi2a ya pia va y2t pi2t yt pit vt ; % Monetary policy rule ia = q1*ya+q2*pia; % ia = q1*(ya-yt)+q2*pia; %%option speed limit policy % Model equations IS = rho*y2a+(1-rho)yt-sigma(ia-pi2a)-ya; AS = beta*pi2a+(1-beta)*pit+alpha*ya-pia+va; dum1 = ya-y2t; dum2 = pia-pi2t; MPs = phi*vt-va; optcon = [IS ; AS ; dum1 ; dum2; MPs]; He then computes the matrix A: %% ------------------ [3] Linearization proc ------------------------%% % Differentiation xx = [y2a pi2a ya pia va y2t pi2t yt pit vt] ; % define vars jopt = jacobian(optcon,xx); % Define Linear Coefficients coef = eval(jopt); B = [ -coef(:,1:5) ] ; C = [ coef(:,6:10) ] ; % B[c(t+1) l(t+1) k(t+1) z(t+1)] = C[c(t) l(t) k(t) z(t)] A = inv(C)*B ; %(Linearized reduced form ) As far as I understand, this A is the solution to the system. It's the matrix that turns time t+1 and t+2 variables into t and t+1 variables (it's a forward-looking model). My question is essentially why is it necessary to reverse the signs of all the partial derivatives in B in order to get this solution? I'm talking about this step: B = [ -coef(:,1:5) ] ; Reversing the sign here obviously reverses the sign of every component of A, but I don't have a clear understanding of why it's necessary. My apologies if the question is unclear or if this isn't the best place to ask.

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  • NET Math Libraries

    - by JoshReuben
    NET Mathematical Libraries   .NET Builder for Matlab The MathWorks Inc. - http://www.mathworks.com/products/netbuilder/ MATLAB Builder NE generates MATLAB based .NET and COM components royalty-free deployment creates the components by encrypting MATLAB functions and generating either a .NET or COM wrapper around them. .NET/Link for Mathematica www.wolfram.com a product that 2-way integrates Mathematica and Microsoft's .NET platform call .NET from Mathematica - use arbitrary .NET types directly from the Mathematica language. use and control the Mathematica kernel from a .NET program. turns Mathematica into a scripting shell to leverage the computational services of Mathematica. write custom front ends for Mathematica or use Mathematica as a computational engine for another program comes with full source code. Leverages MathLink - a Wolfram Research's protocol for sending data and commands back and forth between Mathematica and other programs. .NET/Link abstracts the low-level details of the MathLink C API. Extreme Optimization http://www.extremeoptimization.com/ a collection of general-purpose mathematical and statistical classes built for the.NET framework. It combines a math library, a vector and matrix library, and a statistics library in one package. download the trial of version 4.0 to try it out. Multi-core ready - Full support for Task Parallel Library features including cancellation. Broad base of algorithms covering a wide range of numerical techniques, including: linear algebra (BLAS and LAPACK routines), numerical analysis (integration and differentiation), equation solvers. Mathematics leverages parallelism using .NET 4.0's Task Parallel Library. Basic math: Complex numbers, 'special functions' like Gamma and Bessel functions, numerical differentiation. Solving equations: Solve equations in one variable, or solve systems of linear or nonlinear equations. Curve fitting: Linear and nonlinear curve fitting, cubic splines, polynomials, orthogonal polynomials. Optimization: find the minimum or maximum of a function in one or more variables, linear programming and mixed integer programming. Numerical integration: Compute integrals over finite or infinite intervals, over 2D and higher dimensional regions. Integrate systems of ordinary differential equations (ODE's). Fast Fourier Transforms: 1D and 2D FFT's using managed or fast native code (32 and 64 bit) BigInteger, BigRational, and BigFloat: Perform operations with arbitrary precision. Vector and Matrix Library Real and complex vectors and matrices. Single and double precision for elements. Structured matrix types: including triangular, symmetrical and band matrices. Sparse matrices. Matrix factorizations: LU decomposition, QR decomposition, singular value decomposition, Cholesky decomposition, eigenvalue decomposition. Portability and performance: Calculations can be done in 100% managed code, or in hand-optimized processor-specific native code (32 and 64 bit). Statistics Data manipulation: Sort and filter data, process missing values, remove outliers, etc. Supports .NET data binding. Statistical Models: Simple, multiple, nonlinear, logistic, Poisson regression. Generalized Linear Models. One and two-way ANOVA. Hypothesis Tests: 12 14 hypothesis tests, including the z-test, t-test, F-test, runs test, and more advanced tests, such as the Anderson-Darling test for normality, one and two-sample Kolmogorov-Smirnov test, and Levene's test for homogeneity of variances. Multivariate Statistics: K-means cluster analysis, hierarchical cluster analysis, principal component analysis (PCA), multivariate probability distributions. Statistical Distributions: 25 29 continuous and discrete statistical distributions, including uniform, Poisson, normal, lognormal, Weibull and Gumbel (extreme value) distributions. Random numbers: Random variates from any distribution, 4 high-quality random number generators, low discrepancy sequences, shufflers. New in version 4.0 (November, 2010) Support for .NET Framework Version 4.0 and Visual Studio 2010 TPL Parallellized – multicore ready sparse linear program solver - can solve problems with more than 1 million variables. Mixed integer linear programming using a branch and bound algorithm. special functions: hypergeometric, Riemann zeta, elliptic integrals, Frensel functions, Dawson's integral. Full set of window functions for FFT's. Product  Price Update subscription Single Developer License $999  $399  Team License (3 developers) $1999  $799  Department License (8 developers) $3999  $1599  Site License (Unlimited developers in one physical location) $7999  $3199    NMath http://www.centerspace.net .NET math and statistics libraries matrix and vector classes random number generators Fast Fourier Transforms (FFTs) numerical integration linear programming linear regression curve and surface fitting optimization hypothesis tests analysis of variance (ANOVA) probability distributions principal component analysis cluster analysis built on the Intel Math Kernel Library (MKL), which contains highly-optimized, extensively-threaded versions of BLAS (Basic Linear Algebra Subroutines) and LAPACK (Linear Algebra PACKage). Product  Price Update subscription Single Developer License $1295 $388 Team License (5 developers) $5180 $1554   DotNumerics http://www.dotnumerics.com/NumericalLibraries/Default.aspx free DotNumerics is a website dedicated to numerical computing for .NET that includes a C# Numerical Library for .NET containing algorithms for Linear Algebra, Differential Equations and Optimization problems. The Linear Algebra library includes CSLapack, CSBlas and CSEispack, ports from Fortran to C# of LAPACK, BLAS and EISPACK, respectively. Linear Algebra (CSLapack, CSBlas and CSEispack). Systems of linear equations, eigenvalue problems, least-squares solutions of linear systems and singular value problems. Differential Equations. Initial-value problem for nonstiff and stiff ordinary differential equations ODEs (explicit Runge-Kutta, implicit Runge-Kutta, Gear's BDF and Adams-Moulton). Optimization. Unconstrained and bounded constrained optimization of multivariate functions (L-BFGS-B, Truncated Newton and Simplex methods).   Math.NET Numerics http://numerics.mathdotnet.com/ free an open source numerical library - includes special functions, linear algebra, probability models, random numbers, interpolation, integral transforms. A merger of dnAnalytics with Math.NET Iridium in addition to a purely managed implementation will also support native hardware optimization. constants & special functions complex type support real and complex, dense and sparse linear algebra (with LU, QR, eigenvalues, ... decompositions) non-uniform probability distributions, multivariate distributions, sample generation alternative uniform random number generators descriptive statistics, including order statistics various interpolation methods, including barycentric approaches and splines numerical function integration (quadrature) routines integral transforms, like fourier transform (FFT) with arbitrary lengths support, and hartley spectral-space aware sequence manipulation (signal processing) combinatorics, polynomials, quaternions, basic number theory. parallelized where appropriate, to leverage multi-core and multi-processor systems fully managed or (if available) using native libraries (Intel MKL, ACMS, CUDA, FFTW) provides a native facade for F# developers

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  • How can i interpret a time value in ascii into a numerical value?

    - by Bilal
    I have a file which is as follows: 15:03:21 II 0.88 0.64 15:03:31 II 0.88 0.64 15:03:42 II 0.40 0.40 etc. after loading the file in matlab, I want to be able to read the first column (which corresponds to time) and interpret them as numerical values. At the moment, they are interpreted as a string of ascii characters and i can't perform any mathematical operations on them. Does anyone have any suggestions as to how i can read the time as numbers instead of a string of ascii characters?

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  • What is this "Change to Display" of math equations and why does it change the equation style in Word 2010?

    - by ysap
    I am writing an equation with the "new" Equation Editor in MS Word 2010 (Insert - Equation). When using one of the "large operators", for example the Sigma, with lower and upper limits, there are two styles for displaying the limits - below and above the Sigma, or to the right as super/subscripts. I am choosing the first style - limits above and below to get the standard notation, but Word formats the equation the other way. Now, the object has a bounding box with a context menu on its right. In this menu, I can select Change to Display and the equation is moved to a new line, w/o adjacent text - but, now the sigma limits appear as requested! Then, selecting Change to Inline reverts to the previous form. So, I want to know if there is away to force the requested form with an "inline" attribute? I know that I can use a MS Equation 3.0 object, but I want to remain with the new, "native" editor.

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  • How to create a NSPredicate to find entries with leading numerical value?

    - by Toastor
    Hello, I'm using NSPredicates to fetch entities based on a name attribute. Creating a predicate for names beginning with letters was easy (@"name BEGINSWITH %@", searchLetter), however now I'd like to fetch all entities with a name that begins with a numerical value, or rather a non-alphabetical number. What would be the appropriate predicate expression here? Right now I don't want to get too deep into predicate programming, as this is all I need right now and time flies. So, please, don't point me to the Predicate Programming Guide, I just need that expression.. :) Thanks alot guys!

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  • opath syntax to force dynamic distribution group field as numerical comparison? (Exchange 2010)

    - by Matt
    I'm upgrading a (working) query based group (Exchange 2003) to a new and 'improved' dynamic distribution group (2010). For better or worse, our company decided to store everyone's employee ID in the pager field, so it's easy to manipulate via ADUC. That employee number has significance, as all employees are in a certain range, and all contractors are in a very different range. Basically, the new opath syntax appears to be using string compare on my pager field, even though it's a number. Let's say my employee ID is 3004, well, it's "less than" 4 from a string check POV. Set-DynamicDistributionGroup -Identity "my-funky-new-group" -RecipientFilter "(pager -lt 4) -and (pager -like '*') -and (RecipientType -eq 'UserMailbox')" Shows up in EMC with this: ((((((Pager -lt '4') -and (Pager -ne $null))) -and (RecipientType -eq 'UserMailbox'))) -and (-not(Name -like 'SystemMailbox{*')) -and (-not(Name -like 'CAS_{*')) -and (-not(RecipientTypeDetailsValue -eq 'MailboxPlan')) -and (-not(RecipientTypeDetailsValue -eq 'DiscoveryMailbox')) -and (-not(RecipientTypeDetailsValue -eq 'ArbitrationMailbox'))) This group should have max of 3 members right? Nope - I get a ton because of the string compare. I show up, and I'm in the 3000 range. Question: Anyone know a clever way to force this to be an integer check? The read-only LDAP filter on this group looks good, but of course it can't be edited. The LDAP representation (look ma, no quotes on the 4!) - Also interesting it sort of 'fills the' bed with the (pager=4) thing... (&(pager<=4)(!(pager=4))(pager=*)(objectClass=user)(objectCategory=person)(mailNickname=*)(msExchHomeServerName=*)(!(name=SystemMailbox{*))(!(name=CAS_{*))!(msExchRecipientTypeDetails=16777216))(!(msExchRecipientTypeDetails=536870912))(!(msExchRecipientTypeDetails=8388608))) If there is no solution, I suppose my recourse is either finding an unused field that actually will be treated as an integer, or most likely building this list with powershell every morning with my own automation - lame. I know of a few ways to fix this outside of the opath filter (designate "full-time" in another field, etc.), but would rather exchange do the lifting since this is the environment at the moment. Any insight would be great - thanks! Matt

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  • What statistics can be maintained for a set of numerical data without iterating?

    - by Dan Tao
    Update Just for future reference, I'm going to list all of the statistics that I'm aware of that can be maintained in a rolling collection, recalculated as an O(1) operation on every addition/removal (this is really how I should've worded the question from the beginning): Obvious Count Sum Mean Max* Min* Median** Less Obvious Variance Standard Deviation Skewness Kurtosis Mode*** Weighted Average Weighted Moving Average**** OK, so to put it more accurately: these are not "all" of the statistics I'm aware of. They're just the ones that I can remember off the top of my head right now. *Can be recalculated in O(1) for additions only, or for additions and removals if the collection is sorted (but in this case, insertion is not O(1)). Removals potentially incur an O(n) recalculation for non-sorted collections. **Recalculated in O(1) for a sorted, indexed collection only. ***Requires a fairly complex data structure to recalculate in O(1). ****This can certainly be achieved in O(1) for additions and removals when the weights are assigned in a linearly descending fashion. In other scenarios, I'm not sure. Original Question Say I maintain a collection of numerical data -- let's say, just a bunch of numbers. For this data, there are loads of calculated values that might be of interest; one example would be the sum. To get the sum of all this data, I could... Option 1: Iterate through the collection, adding all the values: double sum = 0.0; for (int i = 0; i < values.Count; i++) sum += values[i]; Option 2: Maintain the sum, eliminating the need to ever iterate over the collection just to find the sum: void Add(double value) { values.Add(value); sum += value; } void Remove(double value) { values.Remove(value); sum -= value; } EDIT: To put this question in more relatable terms, let's compare the two options above to a (sort of) real-world situation: Suppose I start listing numbers out loud and ask you to keep them in your head. I start by saying, "11, 16, 13, 12." If you've just been remembering the numbers themselves and nothing more, and then I say, "What's the sum?", you'd have to think to yourself, "OK, what's 11 + 16 + 13 + 12?" before responding, "52." If, on the other hand, you had been keeping track of the sum yourself while I was listing the numbers (i.e., when I said, "11" you thought "11", when I said "16", you thought, "27," and so on), you could answer "52" right away. Then if I say, "OK, now forget the number 16," if you've been keeping track of the sum inside your head you can simply take 16 away from 52 and know that the new sum is 36, rather than taking 16 off the list and them summing up 11 + 13 + 12. So my question is, what other calculations, other than the obvious ones like sum and average, are like this? SECOND EDIT: As an arbitrary example of a statistic that (I'm almost certain) does require iteration -- and therefore cannot be maintained as simply as a sum or average -- consider if I asked you, "how many numbers in this collection are divisible by the min?" Let's say the numbers are 5, 15, 19, 20, 21, 25, and 30. The min of this set is 5, which divides into 5, 15, 20, 25, and 30 (but not 19 or 21), so the answer is 5. Now if I remove 5 from the collection and ask the same question, the answer is now 2, since only 15 and 30 are divisible by the new min of 15; but, as far as I can tell, you cannot know this without going through the collection again. So I think this gets to the heart of my question: if we can divide kinds of statistics into these categories, those that are maintainable (my own term, maybe there's a more official one somewhere) versus those that require iteration to compute any time a collection is changed, what are all the maintainable ones? What I am asking about is not strictly the same as an online algorithm (though I sincerely thank those of you who introduced me to that concept). An online algorithm can begin its work without having even seen all of the input data; the maintainable statistics I am seeking will certainly have seen all the data, they just don't need to reiterate through it over and over again whenever it changes.

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  • What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

    - by Ein Doofus
    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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  • Disable MathML output of eLyXer

    - by Gryllida
    eLyXer is a standalone LyX to HTML converter. In the resulting file, equations are formatted as MathML, and the file itself starts with an XML tag. This causes two problems: LibreOffice does not read the XML file (it can read HTML files, but not XHTML). I am unable to copy and paste the equations into a document editor such as LibreOffice with the goal of subsequent conversion into .doc, because .doc files do not support MathML. The eLyXer help page mentions an option to only use simple math, but there is no option to set math equations to output as images. And I already set Document Settings Output Math equations Format: images in LyX, which presumably is saved in the lyx document somewhere. A web search did not come up with any solutions.

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