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• What is the simplest way to interpolate and lookup in an x,y table in excel?

  - by dassouki

  I would like to do a lookup and interpolation based on x, y data for the following table. I'd like the equation to be as simple as possible to reduce the amount of possible errors. The full table is about 50 rows x 30 columns. I have about 20 of those tables. Here is an extract from one: A B C D 1 0.1 0.2 0.3 2 2.4 450 300 50 3 2.3 500 375 52 4 2.1 550 475 55 5 1.8 600 600 60 For example, the equation should find the value for x = 2.27 and y = 0.15

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• Sample uniformly at random from an n-dimensional unit simplex.

  - by dreeves

  Sampling uniformly at random from an n-dimensional unit simplex is the fancy way to say that you want n random numbers such that they are all non-negative, they sum to one, and every possible vector of n non-negative numbers that sum to one are equally likely. In the n=2 case you want to sample uniformly from the segment of the line x+y=1 (ie, y=1-x) that is in the positive quadrant. In the n=3 case you're sampling from the triangle-shaped part of the plane x+y+z=1 that is in the positive octant of R3: (Image from http://en.wikipedia.org/wiki/Simplex.) Note that picking n uniform random numbers and then normalizing them so they sum to one does not work. You end up with a bias towards less extreme numbers. Similarly, picking n-1 uniform random numbers and then taking the nth to be one minus the sum of them also introduces bias. Wikipedia gives two algorithms to do this correctly: http://en.wikipedia.org/wiki/Simplex#Random_sampling (Though the second one currently claims to only be correct in practice, not in theory. I'm hoping to clean that up or clarify it when I understand this better. I initially stuck in a "WARNING: such-and-such paper claims the following is wrong" on that Wikipedia page and someone else turned it into the "works only in practice" caveat.) Finally, the question: What do you consider the best implementation of simplex sampling in Mathematica (preferably with empirical confirmation that it's correct)? Related questions http://stackoverflow.com/questions/2171074/generating-a-probability-distribution http://stackoverflow.com/questions/3007975/java-random-percentages

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• Curve fitting: Find the smoothest function that satisfies a list of constraints.

  - by dreeves

  Consider the set of non-decreasing surjective (onto) functions from (-inf,inf) to [0,1]. (Typical CDFs satisfy this property.) In other words, for any real number x, 0 <= f(x) <= 1. The logistic function is perhaps the most well-known example. We are now given some constraints in the form of a list of x-values and for each x-value, a pair of y-values that the function must lie between. We can represent that as a list of {x,ymin,ymax} triples such as constraints = {{0, 0, 0}, {1, 0.00311936, 0.00416369}, {2, 0.0847077, 0.109064}, {3, 0.272142, 0.354692}, {4, 0.53198, 0.646113}, {5, 0.623413, 0.743102}, {6, 0.744714, 0.905966}} Graphically that looks like this: We now seek a curve that respects those constraints. For example: Let's first try a simple interpolation through the midpoints of the constraints: mids = ({#1, Mean[{#2,#3}]}&) @@@ constraints f = Interpolation[mids, InterpolationOrder->0] Plotted, f looks like this: That function is not surjective. Also, we'd like it to be smoother. We can increase the interpolation order but now it violates the constraint that its range is [0,1]: The goal, then, is to find the smoothest function that satisfies the constraints: Non-decreasing. Tends to 0 as x approaches negative infinity and tends to 1 as x approaches infinity. Passes through a given list of y-error-bars. The first example I plotted above seems to be a good candidate but I did that with Mathematica's FindFit function assuming a lognormal CDF. That works well in this specific example but in general there need not be a lognormal CDF that satisfies the constraints.

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• Convert a Dynamic[] construct to a numerical list

  - by Leo Alekseyev

  I have been trying to put together something that allows me to extract points from a ListPlot in order to use them in further computations. My current approach is to select points with a Locator[]. This works fine for displaying points, but I cannot figure out how to extract numerical values from a construct with head Dynamic[]. Below is a self-contained example. By dragging the gray locator, you should be able to select points (indicated by the pink locator and stored in q, a list of two elements). This is the second line below the plot. Now I would like to pass q[[2]] to a function, or perhaps simply display it. However, Mathematica treats q as a single entity with head Dynamic, and thus taking the second part is impossible (hence the error message). Can anyone shed light on how to convert q into a regular list? EuclideanDistanceMod[p1_List, p2_List, fac_: {1, 1}] /; Length[p1] == Length[p2] := Plus @@ (fac.MapThread[Abs[#1 - #2]^2 &, {p1, p2}]) // Sqrt; test1 = {{1.`, 6.340196001221532`}, {1.`, 13.78779876355869`}, {1.045`, 6.2634018978377295`}, {1.045`, 13.754947081416544`}, {1.09`, 6.178367702583522`}, {1.09`, 13.72055251752498`}, {1.135`, 1.8183153704413153`}, {1.135`, 6.082497198000075`}, {1.135`, 13.684582525399742`}, {1.18`, 1.6809452373465104`}, {1.18`, 5.971583107298081`}, {1.18`, 13.646996905469383`}, {1.225`, 1.9480537697339537`}, {1.225`, 5.838386922625636`}, {1.225`, 13.607746407088161`}, {1.27`, 2.1183174369679234`}, {1.27`, 5.669799095595362`}, {1.27`, 13.566771130126131`}, {1.315`, 2.2572975468163463`}, {1.315`, 5.444014254828522`}, {1.315`, 13.523998701347882`}, {1.36`, 2.380307009155079`}, {1.36`, 5.153024664297602`}, {1.36`, 13.479342200528283`}, {1.405`, 2.4941312539733285`}, {1.405`, 4.861423833512566`}, {1.405`, 13.432697814928654`}, {1.45`, 2.6028066447609426`}, {1.45`, 4.619367407525507`}, {1.45`, 13.383942212133244`}}; DynamicModule[{p = {1.2, 10}, q = {1.3, 11}}, q := Dynamic@ First@test1[[ Ordering[{#, EuclideanDistanceMod[p, #, {1, .1}]} & /@ test1, 1, #1[[2]] < #2[[2]] &]]]; Grid[{{Show[{ListPlot[test1, Frame -> True, ImageSize -> 300], Graphics@Locator[Dynamic[p]], Graphics@ Locator[q, Appearance -> {Small}, Background -> Pink]}]}, {Dynamic@p}, {q},{q[[2]]}}]]

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• ReplaceAll not working as expected

  - by Tim Kemp

  Still early days with Mathematica so please forgive what is probably a very obvious question. I am trying to generate some parametric plots. I have: ParametricPlot[{ (a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, {t, 0, 2 \[Pi]}, PlotRange -> All] /. {a -> 2, b -> 1, h -> 1} No joy: the replacement rules are not applied and a, b and h remain undefined. If I instead do: Hold@ParametricPlot[{ (a + b) Cos[t] - h Cos[(a + b)/b t], (a + b) Sin[t] - h Sin[(a + b)/b t]}, {t, 0, 2 \[Pi]}, PlotRange -> All] /. {a -> 2, b -> 1, h -> 1} it looks like the rules ARE working, as confirmed by the output: Hold[ParametricPlot[{(2 + 1) Cos[t] - 1 Cos[(2 + 1) t], (2 + 1) Sin[t] - 1 Sin[(2 + 1) t]}, {t, 0, 2 \[Pi]}, PlotRange -> All]] Which is what I'd expect. Take the Hold off, though, and the ParametricPlot doesn't work. There's nothing wrong with the equations or the ParametricPlot itself, though, because I tried setting values for a, b and h in a separate expression (a=2; b=1; h=1) and I get my pretty double cardoid out as expected. So, what am I doing wrong with ReplaceAll and why are the transformation rules not working? This is another fundamentally important aspect of MMA that my OOP-ruined brain isn't understanding. I tried reading up on ReplaceAll and ParametricPlot and the closest clue I found was that "ParametricPlot has attribute HoldAll and evaluates f only after assigning specific numerical values to variables" which didn't help much or I wouldn't be here. Thanks.

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• Show a number with specified number of significant digits

  - by dreeves

  I use the following function to convert a number to a string for display purposes (don't use scientific notation, don't use a trailing dot, round as specified): (* Show Number. Convert to string w/ no trailing dot. Round to the nearest r. *) Unprotect[Round]; Round[x_,0] := x; Protect[Round]; shn[x_, r_:0] := StringReplace[ ToString@NumberForm[Round[N@x,r], ExponentFunction->(Null&)], re@"\\.$"->""] (Note that re is an alias for RegularExpression.) That's been serving me well for years. But sometimes I don't want to specify the number of digits to round to, rather I want to specify a number of significant figures. For example, 123.456 should display as 123.5 but 0.00123456 should display as 0.001235. To get really fancy, I might want to specify significant digits both before and after the decimal point. For example, I might want .789 to display as 0.8 but 789.0 to display as 789 rather than 800. Do you have a handy utility function for this sort of thing, or suggestions for generalizing my function above? Related: Suppressing a trailing "." in numerical output from Mathematica

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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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• Octave: Multiple submatrices from a matrix

  - by fbrereto

  I have a large matrix from which I would like to gather a collection of submatrices. If my matrix is NxN and the submatrix size is MxM, I want to collect I=(N - M + 1)^2 submatrices. In other words I want one MxM submatrix for each element in the original matrix that can be in the top-left corner of such a matrix. Here's the code I have: for y = 1:I for x = 1:I index = (y - 1) * I + x; block_set(index) = big_mat(x:x+M-1, y:y+M-1) endfor endfor The output if a) wrong, and b) implying there is something in the big_mat(x:x+M-1, y:y+M-1) expression that can get me what I want without needing the two for loops. Any help would be much appreciated

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• Curve fitting: Find a CDF (or any function) that satisfies a list of constraints.

  - by dreeves

  I have some constraints on a CDF in the form of a list of x-values and for each x-value, a pair of y-values that the CDF must lie between. We can represent that as a list of {x,y1,y2} triples such as constraints = {{0, 0, 0}, {1, 0.00311936, 0.00416369}, {2, 0.0847077, 0.109064}, {3, 0.272142, 0.354692}, {4, 0.53198, 0.646113}, {5, 0.623413, 0.743102}, {6, 0.744714, 0.905966}} Graphically that looks like this: And since this is a CDF there's an additional implicit constraint of {Infinity, 1, 1} Ie, the function must never exceed 1. Also, it must be monotone. Now, without making any assumptions about its functional form, we want to find a curve that respects those constraints. For example: (I cheated to get that one: I actually started with a nice log-normal distribution and then generated fake constraints based on it.) One possibility is a straight interpolation through the midpoints of the constraints: mids = ({#1, Mean[{#2,#3}]}&) @@@ constraints f = Interpolation[mids, InterpolationOrder->0] Plotted, f looks like this: That sort of technically satisfies the constraints but it needs smoothing. We can increase the interpolation order but now it violates the implicit constraints (always less than one, and monotone): How can I get a curve that looks as much like the first one above as possible? Note that NonLinearModelFit with a LogNormalDistribution will do the trick in this example but is insufficiently general as sometimes there will sometimes not exist a log-normal distribution satisfying the constraints.

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• If we make a number every millisecond, how much data would we have in a day?

  - by Roger Travis

  I'm a bit confused here... I'm being offered to get into a project, where would be an array of certain sensors, that would give off reading every millisecond ( yes, 1000 reading in a second ). Reading would be a 3 or 4 digit number, for example like 818 or 1529. This reading need to be stored in a database on a server and accessed remotely. I never worked with such big amounts of data, what do you think, how much in terms of MBs reading from one sensor for a day would be?... 4(digits)x1000x60x60x24 ... = 345600000 bits ... right ? about 42 MB per day... doesn't seem too bad, right? therefor a DB of, say, 1 GB, would hold 23 days of info from 1 sensor, correct? I understand that MySQL & PHP probably would not be able to handle it... what would you suggest, maybe some aps? azure? oracle? ... Thansk!

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• Is there a way to force ContourPlot re-check all the points on the each stage of it's recursion algorithm?

  - by Alexey Popkov

  Hello, Thanks to this excellent analysis of the Plot algorithm by Yaroslav Bulatov, I now understand the reason why Plot3D and ContourPlot fail to draw smoothly functions with breaks and discontinuities. For example, in the following case ContourPlot fails to draw contour x^2 + y^2 = 1 at all: ContourPlot[Abs[x^2 + y^2 - 1], {x, -1, 1}, {y, -1, 1}, Contours -> {0}] It is because the algorithm does not go deeply into the region near x^2 + y^2 = 1. It "drops" this region on an initial stage and do not tries to investigate it further. Increasing MaxRecursion does nothing in this sense. And even undocumented option Method -> {Refinement -> {ControlValue -> .01 \[Degree]}} does not help (but makes Plot3D a little bit smoother). The above function is just a simple example. In real life I'm working with very complicated implicit functions that cannot be solved analytically. Is there a way to get ContourPlot to go deeply into such regions near breaks and discontinuities?

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• Unsort: remembering a permutation and undoing it.

  - by dreeves

  Suppose I have a function f that takes a vector v and returns a new vector with the elements transformed in some way. It does that by calling function g that assumes the vector is sorted. So I want f to be defined like so: f[v_] := Module[{s, r}, s = Sort[v]; (* remember the permutation applied in order to sort v *) r = g[s]; Unsort[r] (* apply the inverse of that permutation *) ] What's the best way to do the "Unsort"? Or could we get really fancy and have this somehow work: answer = Unsort[g[Sort[v]]]; ADDED: Let's make this concrete with a toy example. Suppose we want a function f that takes a vector and transforms it by adding to each element the next smallest element, if any. That's easy to write if we assume the vector is sorted, so let's write a helper function g that makes that assumption: g[v_] := v + Prepend[Most@v, 0] Now for the function we really want, f, that works whether or not v is sorted: f[v_] := (* remember the order; sort it; call g on it; put it back in the original order; return it *)

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• 6^x = 5 equation, how to solve it?

  - by Tom

  If it would be 6^x = 1 or 6^x = 6 or 6^x = 36 it would be extremely easy, but how to solve this equation: 6^x = 5 I don't need an answer, I want to find out how to solve equations like this one, I need solution. Thanks.

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• Efficient way to remove empty lists from lists without evaluating held expressions?

  - by Alexey Popkov

  In previous thread an efficient way to remove empty lists ({}) from lists was suggested: Replace[expr, x_List :> DeleteCases[x, {}], {0, Infinity}] Using the Trott-Strzebonski in-place evaluation technique this method can be generalized for working also with held expressions: f1[expr_] := Replace[expr, x_List :> With[{eval = DeleteCases[x, {}]}, eval /; True], {0, Infinity}] This solution is more efficient than the one based on ReplaceRepeated: f2[expr_] := expr //. {left___, {}, right___} :> {left, right} But it has one disadvantage: it evaluates held expressions if they are wrapped by List: In[20]:= f1[Hold[{{}, 1 + 1}]] Out[20]= Hold[{2}] So my question is: what is the most efficient way to remove all empty lists ({}) from lists without evaluating held expressions? The empty List[] object should be removed only if it is an element of another List itself. Here are some timings: In[76]:= expr = Tuples[Tuples[{{}, {}}, 3], 4]; First@Timing[#[expr]] & /@ {f1, f2, f3} pl = Plot3D[Sin[x y], {x, 0, Pi}, {y, 0, Pi}]; First@Timing[#[pl]] & /@ {f1, f2, f3} Out[77]= {0.581, 0.901, 5.027} Out[78]= {0.12, 0.21, 0.18} Definitions: Clear[f1, f2, f3]; f3[expr_] := FixedPoint[ Function[e, Replace[e, {a___, {}, b___} :> {a, b}, {0, Infinity}]], expr]; f1[expr_] := Replace[expr, x_List :> With[{eval = DeleteCases[x, {}]}, eval /; True], {0, Infinity}]; f2[expr_] := expr //. {left___, {}, right___} :> {left, right};

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• Complicated programming and math tasks online. Any?

  - by Tom

  Maybe it is not very thematic question in here, but I guess it will be interesting not only to me. I hope. So, I just want to get some cool tasks to do using programming languages or just pen and sheet of paper. I guess it can lead to improving my ability to do better code (more optimal I mean.) Do you know any websites where I can find it? Thanks.

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• Shuffling a list with a constraint

  - by 500

  Preparing a new psychophysic experiment, I have 48 original stimuli displayed 4 times (4 conditions). Resulting in 192 trials. Trying to randomize the order of presentation during the experiment, I need to maximize the distance between the 4 display of the same original stimuli. Please Consider : Table[{j, i}, {j, Range[48]}, {i, Range[4]}] Where j is the original stimuli number and i the condition Output Sample : {{1, 1}, {1, 2}, {1, 3}, {1, 4}, {2, 1}, {2, 2}, {2, 3}, {2, 4}, ... {47, 1}, {47, 2}, {47, 3},{47, 4}, {48, 1}, {48, 2}, {48, 3}, {48, 4}} How could I shuffle the order of presentation of those 192 items, maximizing the distance between identical item with regard to j the original stimuli number ?

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• Fixing Combinatorica redefinition of Element

  - by Yaroslav Bulatov

  My code relies on version of Element which works like MemberQ, but when I load Combinatorica, Element gets redefined to work like Part. What is the easiest way to fix this conflict? Specifically, what is the syntax to remove Combinatorica's definition from DownValues? Here's what I get for DownValues[Element] {HoldPattern[ Combinatorica`Private`a_List \[Element] \ {Combinatorica`Private`index___}] :> Combinatorica`Private`a[[Combinatorica`Private`index]], HoldPattern[Private`x_ \[Element] Private`list_List] :> MemberQ[Private`list, Private`x]}

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• AbsoluteTime with an integer argument behaves strangely.

  - by dreeves

  This is strange: DateList@AbsoluteTime[596523] returns {2078, 7, 2, 2, 42, 9.7849} But DateList@AbsoluteTime[596524] returns {1942, 5, 26, 20, 28, 39.5596} The question: What's going on? Note that AbsoluteTime with an integer argument is undocumented. (I think I now know what it's doing but figured this is useful to have as a StackOverflow question for future reference; and I'm curious if there's some reason for that magic 596523 number.)

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• 1.6 * 12 * 15 is the volume of some material. How many cubes can be inserted into that?

  - by Neelu

  1.6 * 12 * 15 is the volume of some material. How many cubes can be inserted into that? Can anyone tell me where shall i post this question? Related to mathematics Thanks in advance

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• Best (functional?) programming language to learn coming from Mathematica

  - by Will Robertson

  As a mechanical engineering PhD student, I haven't had a great pedigree in programming as part of my “day job”. I started out in Matlab (having written some Hypercard and Applescript back in the day, and being introduced to Ada, of all things, in my 1st undergrad year), learned to program—if you can call it that—in (La)TeX; and finally discovered and fell for Mathematica. Now I'm interested in learning a "real" programming language that I can enjoy in the same sort of style as Mathematica, which tries to stress functional programming since it seems to map more nicely to how certain kinds of mathematics can be written algorithmically. So which functional language should I learn? I guess the obvious answer is “as many as possible”, but let's start out humble and give a single, well-considered option a good crack. I've heard good things about, say, Haskell and Scala, but I wonder if (given my non–computer science background) I'd be better off starting in more “grounded” territory and going with Ruby or Python (the latter having the big advantage of being used for Sage, which I'd also like to investigate…after my PhD). Well, I guess this is pretty subjective, so perhaps I could rephrase: would it be better to start looking at Haskell (say) straight after an ad-hoc education to functional programming in Mathematica, or will I get more out of learning Python (say) first? In reference to the question "what do I want to do with it?", I guess my answer is "fun, and learning more". I've got this list of languages that I'd like to look at, and I don't know how to trim them down. And I'd rather start with something a little higher-level than C simply so that I can be somewhat productive without having to re-invent many wheels for any code I'd like to write.

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• Pythonika installation error on ubuntu 12

  - by user1426913

  I have been following links: to install pythonika on ubuntu: How to install Pythonika on Ubuntu? I get error: $ sudo make -f Makefile.linux cc -c Pythonika.c -I/usr/local/Wolfram/Mathematica/9.0/SystemFiles/Links/MathLink/DeveloperKit/Linux/CompilerAdditions -I/usr/include/python2.7/ Pythonika.c: In function ‘PyUnicodeString’: Pythonika.c:109:5: warning: passing argument 1 of ‘PyUnicodeUCS4_FromUnicode’ from incompatible pointer type [enabled by default] /usr/include/python2.7/unicodeobject.h:464:23: note: expected ‘const Py_UNICODE *’ but argument is of type ‘short unsigned int *’ Pythonika.c: In function ‘python_to_mathematica_object’: Pythonika.c:411:13: warning: passing argument 2 of ‘MLPutUnicodeString’ from incompatible pointer type [enabled by default] /usr/local/Wolfram/Mathematica/9.0/SystemFiles/Links/MathLink/DeveloperKit/Linux/CompilerAdditions/mathlink.h:4299:1: note: expected ‘const short unsigned int *’ but argument is of type ‘Py_UNICODE ’ "/usr/local/Wolfram/Mathematica/9.0/SystemFiles/Links/MathLink/DeveloperKit/Linux/CompilerAdditions/mprep" Pythonika.tm -o Pythonikatm.c /bin/sh: 1: /usr/local/Wolfram/Mathematica/9.0/SystemFiles/Links/MathLink/DeveloperKit/Linux/CompilerAdditions/mprep: not found make: ** [Pythonikatm.o] Error 127

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• learn the programming language for computing functions about integers

  - by asd

  Hi I know something about Pascal, Mathematica and Matlab, but I dont have any idea about C,C++,C# languages. I want to learn one of the languages that they they are fast and exact to compute some arithmetic functions for large numbers(for example larger than $10^3000$). I asked somebody and he said he used C++ and he said I computed this sequence in less than 10 min. I want to know C, C++, C# and visual kind of theses programs and know which is better for my goal. Let $f$ be an arithmetic function and A={k1,k2,...,kn} are integers in increasing order. Now I want to start with k1 and compare f(ki) with f(k1). If f(ki)f(k1), put ki as k1. Now start with ki, and compare f(kj) with f(ki), for ji. If f(kj)f(ki), put kj as ki, and repeat this procedure. At the end we will have a sub sequence B={L1,...,Lm} of A by this property: f(L(i+1))f(L(i)), for any 1<=i<=m-1 I have written a code for this program with Mathematica, and it take some hours to compute f of ki's or the set B for large numbers. For example, let f is the divisor function of integers. Do you know how to write the code for my purpose in Mathematica or Matlab. Mathematica is preferable.

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• How to interview a natural scientist for a dev position?

  - by Silas

  I already did some interviews for my company, mostly computer scientists for dev positions but also some testers and project managers. Now I have to fill a vacancy in our research group within the R&D department (side note: “research” means that we try to solve problems in our professional domain/market niche using software in research projects together with universities, other companies, research centres and end user organisations. It’s not computer science research; we’re not going to solve the P=NP problem). Now we invited a guy holding an MSc in chemistry (with a lot of physics in his CV, too), who never had any computer science lesson. I already talked with him about half an hour at a local university’s career days and there’s no doubt the guy is smart. Also his marks are excellent and he graduated with distinction. For his BSc he needed to teach himself programming in Mathematica and told me believably that he liked programming a lot. Also he solved some physical chemistry problem that I probably don’t understand using his own software, implemented in Mathematica, for his MSc thesis. It includes a GUI and a notable size of 8,000 LoC. He seems to be very attracted by what we’re doing in our research group and to be honest it’s quite difficult for an SME like us to get good people. I also am very interested in hiring him since he could assist me in writing project proposals, reports, doing presentations and so on. He would probably fit to our team, too. The only question left is: How can I check if he will get the programming skills he needs to do software implementation in our projects since this will be a significant part of the job? Of course I will ask him what it is, that is fascinating him about programming. I’ll also ask how he proceeded to write his natural science software and how he structured it. I’ll ask about how he managed to obtain the skills and information about software development he needed. But is there something more I could ask? Something more concrete perhaps? Should I ask him to explain his Mathematica solution? To be clear: I’m not looking for knowledge in a particular language or technology stack. We’re a .NET shop in product development but I want to have a free choice for our research projects. So I’m interested in the meta-competence being able to learn whatever is actually needed. I hope this question is answerable and not open-ended since I really like to know if there is a default way to check for the ability to get further programming skills on the job. If something is not clear to you please give me some comments and let me improve my question.

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• Help importing .pdb file into Maple

  - by Colin

  I realy know nothing about Maple, so any help would be nice. I am attempting to import a .pdb file into Maple, as part of converting some Mathematica code to Maple. I need something that that can accomplish something equivalent to the Import command in Mathematica. I have tried using readdata, ImportData and fopen with little success. If anyone has any suggestions, that would be of great help.

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• How to calculate the cycles that change one permutation into another?

  - by fortran

  Hi, I'm looking for an algorithm that given two permutations of a sequence (e.g. [2, 3, 1, 4] and [4, 1, 3, 2]) calculates the cycles that are needed to convert the first into the second (for the example, [[0, 3], [1, 2]]). The link from mathworld says that Mathematica's ToCycle function does that, but sadly I don't have any Mathematica license at hand... I'd gladly receive any pointer to an implementation of the algorithm in any FOSS language or mathematics package. Thanks!

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