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  • Optimizing mathematics on arrays of floats in Ada 95 with GNATC

    - by mat_geek
    Consider the bellow code. This code is supposed to be processing data at a fixed rate, in one second batches, It is part of an overal system and can't take up too much time. When running over 100 lots of 1 seconds worth of data the program takes 35 seconds; or 35%. How do I improce the code to get the processing time down to a minimum? The code will be running on an Intel Pentium-M which is a P3 with SSE2. package FF is new Ada.Numerics.Generic_Elementary_Functions(Float); N : constant Integer := 820; type A is array(1 .. N) of Float; type A3 is array(1 .. 3) of A; procedure F(state : in out A3; result : out A3; l : in A; r : in A) is s : Float; t : Float; begin for i in 1 .. N loop t := l(i) + r(i); t := t / 2.0; state(1)(i) := t; state(2)(i) := t * 0.25 + state(2)(i) * 0.75; state(3)(i) := t * 1.0 /64.0 + state(2)(i) * 63.0 /64.0; for r in 1 .. 3 loop s := state(r)(i); t := FF."**"(s, 6.0) + 14.0; if t > MAX then t := MAX; elsif t < MIN then t := MIN; end if; result(r)(i) := FF.Log(t, 2.0); end loop; end loop; end;

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  • Typesetting LaTeX fraction terms to be larger in an equation

    - by gotgenes
    I have the following formula in LaTeX, based on Fisher's Exact Test. (NOTE: requires the use of the amsmath package for \binom.) \begin{equation} P(i,j) = \sum_{x=|N(V_i) \cap V_j|}^{\min\{|V_j|, |N(V_i)|} \frac{ \binom{|V_j|}{x} \binom{|V - V_j|}{|N(V_i)| - x}} {\binom{|V|}{|N(V_i)|}} \end{equation} This renders the fraction portion with very small, difficult to read text: I would like my text more readable, as in the following example: What trickery can I use to get LaTeX to render my equation similarly?

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  • Optimizing mathematics on arrays of floats in Ada 95 with GNAT

    - by mat_geek
    Consider the bellow code. This code is supposed to be processing data at a fixed rate, in one second batches, It is part of an overal system and can't take up too much time. When running over 100 lots of 1 seconds worth of data the program takes 35 seconds (or 35%), executing this function in a loop. The test loop is timed specifically with Ada.RealTime. The data is pregenerated so the majority of the execution time is definatetly in this loop. How do I improce the code to get the processing time down to a minimum? The code will be running on an Intel Pentium-M which is a P3 with SSE2. package FF is new Ada.Numerics.Generic_Elementary_Functions(Float); N : constant Integer := 820; type A is array(1 .. N) of Float; type A3 is array(1 .. 3) of A; procedure F(state : in out A3; result : out A3; l : in A; r : in A) is s : Float; t : Float; begin for i in 1 .. N loop t := l(i) + r(i); t := t / 2.0; state(1)(i) := t; state(2)(i) := t * 0.25 + state(2)(i) * 0.75; state(3)(i) := t * 1.0 /64.0 + state(2)(i) * 63.0 /64.0; for r in 1 .. 3 loop s := state(r)(i); t := FF."**"(s, 6.0) + 14.0; if t > MAX then t := MAX; elsif t < MIN then t := MIN; end if; result(r)(i) := FF.Log(t, 2.0); end loop; end loop; end; psuedocode for testing create two arrays of 80 random A3 arrays, called ls and rs; init the state and result A3 array record the realtime time now, called last for i in 1 .. 100 loop for j in 1 .. 80 loop F(state, result, ls(j), rs(j)); end loop; end loop; record the realtime time now, called curr output the duration between curr and last

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  • Rendering LaTeX on third-party websites?

    - by A. Rex
    There are some sites on the web that render LaTeX into some more readable form, such as Wikipedia, some Wordpress blogs, and MathOverflow. They may use images, MathML, jsMath, or something like that. There are other sites on the web where LaTeX appears inline and is not rendered, such as the arXiv, various math forums, or my email. In fact, it is quite common to see an arXiv paper's abstract with raw LaTeX in it, e.g. this paper. Is there a plugin available for Firefox, or would it be possible to write one, that renders LaTeX within pages that do not provide a rendering mechanism themselves? (The LaTeX would be enclosed within dollar signs, e.g. $\pi$. See the arXiv link above.) Some notes: It may be impossible to render some of the code, because authors often copy-paste code directly from their source TeX files, which may contain things like "\cite{foo}" or undefined commands. These should be left alone. This question is a repost of a question from MathOverflow that was closed for not being related to math. There is one answer there, which is helpful, but perhaps Stack Overflow can provide better answers. I program a lot, but Javascript is not my specialty, so comments along the lines of "look at this library" are not particularly helpful to me (but may be to others).

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  • Code optimization on minutes pr hour calculation

    - by corger
    Hi All, The following code takes a timeframe in minutes since midnight and creates an array with minutes pr hour. But, it's slow. Any better suggestions out there? (no, changing language is not an option :-) ) Const clDeparture As Long = 123 Const clArrival As Long = 233 Dim lHour As Long Dim lMinute As Long Dim alHour(25) As Long For lMinute = 0 To 1440 If lMinute >= clDeparture And lMinute < clArrival Then alHour(Int(lMinute / 60)) = alHour(Int(lMinute / 60)) + 1 End If Next The array should now contain: (0,0) (1,0) (2,57) (3,53) (4,0) ..... Regards

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  • What is a data structure for quickly finding non-empty intersections of a list of sets?

    - by Andrey Fedorov
    I have a set of N items, which are sets of integers, let's assume it's ordered and call it I[1..N]. Given a candidate set, I need to find the subset of I which have non-empty intersections with the candidate. So, for example, if: I = [{1,2}, {2,3}, {4,5}] I'm looking to define valid_items(items, candidate), such that: valid_items(I, {1}) == {1} valid_items(I, {2}) == {1, 2} valid_items(I, {3,4}) == {2, 3} I'm trying to optimize for one given set I and a variable candidate sets. Currently I am doing this by caching items_containing[n] = {the sets which contain n}. In the above example, that would be: items_containing = [{}, {1}, {1,2}, {2}, {3}, {3}] That is, 0 is contained in no items, 1 is contained in item 1, 2 is contained in itmes 1 and 2, 2 is contained in item 2, 3 is contained in item 2, and 4 and 5 are contained in item 3. That way, I can define valid_items(I, candidate) = union(items_containing[n] for n in candidate). Is there any more efficient data structure (of a reasonable size) for caching the result of this union? The obvious example of space 2^N is not acceptable, but N or N*log(N) would be.

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  • Mathematics - Why is Differential Calculus (MVP) in PHP a tabu?

    - by Email
    Hi I want to do a Mean-Variance-Optimization (Markowitz) but i never found anything written in php that does this. MVP needs differential calculus. Can it be done in php and why arent there any classes/works from universities? For a webapplication (regarding performance) would another language be the better choice to handle heavy calculations? Thanks so much for any help/answer on this

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  • Adding an equation or formula to a figure caption in LaTeX

    - by gotgenes
    I have a figure in LaTeX with a caption to which I need to add a formula (equation* or displaymath environments). For example: \documentclass[12pt]{article} \begin{document} \begin{figure}[tbph] \begin{center} %... \end{center} \caption{As you can see \begin{displaymath}4 \ne 5\end{displaymath} } \label{fig:somefig} \end{figure} \end{document} This makes pdflatex angry, though it will produce a PDF. ! Argument of \@caption has an extra }. <inserted text> \par l.9 } What's the right way to go about adding an equation to a figure caption? NOTE: Please do not suggest simply using the $ ... $ math environment; the equation shown is a toy example; my real equation is much more intricate. See also: Adding a caption to an equation in LaTeX (the reverse of this question)

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  • How to use constraint programming for optimizing shopping baskets?

    - by tangens
    I have a list of items I want to buy. The items are offered by different shops and different prices. The shops have individual delivery costs. I'm looking for an optimal shopping strategy (and a java library supporting it) to purchase all of the items with a minimal total price. Example: Item1 is offered at Shop1 for $100, at Shop2 for $111. Item2 is offered at Shop1 for $90, at Shop2 for $85. Delivery cost of Shop1: $10 if total order < $150; $0 otherwise Delivery cost of Shop2: $5 if total order < $50; $0 otherwise If I buy Item1 and Item2 at Shop1 the total cost is $100 + $90 +$0 = $190. If I buy Item1 and Item2 at Shop2 the total cost is $111 + $85 +$0 = $196. If I buy Item1 at Shop1 and Item2 at Shop2 the total cost is $100 + $10 + $85 + $0 = 195. I get the minimal price if I order Item1 and Item2 at Shop1: $190 What I tried so far I asked another question before that led me to the field of constraint programming. I had a look at cream and choco, but I did not figure out how to create a model to solve my problem. | shop1 | shop2 | shop3 | ... ----------------------------------------- item1 | p11 | p12 | p13 | item2 | p21 | p22 | p23 | . | | | | . | | | | ----------------------------------------- shipping | s1 | s2 | s3 | limit | l1 | l2 | l3 | ----------------------------------------- total | t1 | t2 | t3 | ----------------------------------------- My idea was to define these constraints: each price "p xy" is defined in the domain (0, c) where c is the price of the item in this shop only one price in a line should be non zero if one or more items are bought from one shop and the sum of the prices is lower than limit, then add shipping cost to the total cost shop total cost is the sum of the prices of all items in a shop total cost is the sum of all shop totals The objective is "total cost". I want to minimize this. In cream I wasn't able to express the "if then" constraint for conditional shipping costs. In choco these constraints exist, but even for 5 items and 10 shops the program was running for 10 minutes without finding a solution. Question How should I express my constraints to make this problem solvable for a constraint programming solver?

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  • why do we need advanced knowledge of mathematics & physics for programming?

    - by Sumeet
    Guys, I have been very good in mathematics and physics in my schools and colleges. Right now I am a programmer. Even in the colleges I have to engrossed my self into computers and programming things all the time. As I used to like it very much. But I have always felt the lack of advanced mathematics and physics in all the work I have done (Programs). Programming never asked me any advanced mathematics and physics knowledge in what I was very good. It always ask u some optimized loops, and different programming technologies which has never been covered in advanced mathematics and physics. Even at the time of selection in big College , such a kind of advanced knowledge is required. Time by time I got out of touch of all that facts and concepts (advanced mathematics and physics). And now after, 5 years in job I found it hard to resolve Differentiations and integrations from Trigonometry. Which sometimes make me feel like I have wasted time in those concepts because they are never used. (At that time I knew that I am going to be a programmer) If one need to be a programmer why do all this advanced knowledge is required. One can go with elementry knowledge a bit more. You never got to think like scientists and R&D person in your Schols and colleges for being a programmer? Just think and let me know your thoughts. I must be wrong somewhere in what I think , but not able to figure that out..? Regards Sumeet

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  • What's the fastest way to approximate the period of data using Octave?

    - by John
    I have a set of data that is periodic (but not sinusoidal). I have a set of time values in one vector and a set of amplitudes in a second vector. I'd like to quickly approximate the period of the function. Any suggestions? Specifically, here's my current code. I'd like to approximate the period of the vector x(:,2) against the vector t. Ultimately, I'd like to do this for lots of initial conditions and calculate the period of each and plot the result. function xdot = f (x,t) xdot(1) =x(2); xdot(2) =-sin(x(1)); endfunction x0=[1;1.75]; #eventually, I'd like to try lots of values for x0(2) t = linspace (0, 50, 200); x = lsode ("f", x0, t) plot(x(:,1),x(:,2)); Thank you! John

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  • Efficient implementation of natural logarithm (ln) and exponentiation

    - by Donotalo
    Basically, I'm looking for implementation of log() and exp() functions provided in C library <math.h>. I'm working with 8 bit microcontrollers (OKI 411 and 431). I need to calculate Mean Kinetic Temperature. The requirement is that we should be able to calculate MKT as fast as possible and with as little code memory as possible. The compiler comes with log() and exp() functions in <math.h>. But calling either function and linking with the library causes the code size to increase by 5 Kilobytes, which will not fit in one of the micro we work with (OKI 411), because our code already consumed ~12K of available ~15K code memory. The implementation I'm looking for should not use any other C library functions (like pow(), sqrt() etc). This is because all library functions are packed in one library and even if one function is called, the linker will bring whole 5K library to code memory.

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  • optimized grid for rectangular items

    - by peterchen
    I have N rectangular items with an aspect ratio Aitem (X:Y). I have a rectangular display area with an aspect ratio Aview The items should be arranged in a table-like layout (i.e. r rows, c columns). what is the ideal grid rows x columns, so that individual items are largest? (rows * colums = N, of course - i.e. there may be "unused" grid places). A simple algorithm could iterate over rows = 1..N, calculate the required number of columns, and keep the row/column pair with the largest items. I wonder if there's a non-iterative algorithm, though (e.g. for Aitem = Aview = 1, rows / cols can be approximated by sqrt(N)).

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  • How computer multiplies 2 numbers?

    - by ckv
    How does a computer perform a multiplication on 2 numbers say 100 * 55. My guess was that the computer did repeated addition to achieve multiplication. Of course this could be the case for integer numbers. However for floating point numbers there must be some other logic. Note: This was asked in an interview.

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  • Merging and splitting overlapping rectangles to produce non-overlapping ones

    - by uj
    I am looking for an algorithm as follows: Given a set of possibly overlapping rectangles (All of which are "not rotated", can be uniformly represented as (left,top,right,bottom) tuplets, etc...), it returns a minimal set of (non-rotated) non-overlapping rectangles, that occupy the same area. It seems simple enough at first glance, but prooves to be tricky (at least to be done efficiently). Are there some known methods for this/ideas/pointers? Methods for not necessarily minimal, but heuristicly small, sets, are interesting as well, so are methods that produce any valid output set at all.

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  • Getting confused why i dont get expected amount ?

    - by Stackfan
    I have 1 result and which i will receive in Bank account, Based on that account i have to Put a balance to user account. How can you find the Handling cost from total tried 491.50 / 0.95 = 517.36 which is wrong ? It should be 500.00 (to my expectation) User balance requires 500.00 When 500.00 selected he gets 5% discount There is a handling cost for this ex: 1) Discount: 500.00 - 5% = 475.00 2) Handling cost: (475.00 x 0.034) + 0.35 = 16.50 3) Total: 475.00 + 16.50 = 491.50 So problem is from 491.50, i have to find atleast handling cost to get promised Balance. Any solution ? Cant figure it out myself...

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  • Speeding up Math calculations in Java

    - by Simon
    I have a neural network written in Java which uses a sigmoid transfer function defined as follows: private static double sigmoid(double x) { return 1 / (1 + Math.exp(-x)); } and this is called many times during training and computation using the network. Is there any way of speeding this up? It's not that it's slow, it's just that it is used a lot, so a small optimisation here would be a big overall gain.

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  • Wpf. Chart optimization. More than million points

    - by Evgeny
    I have custom control - chart with size, for example, 300x300 pixels and more than one million points (maybe less) in it. And its clear that now he works very slowly. I am searching for algoritm which will show only few points with minimal visual difference. I have link to component which have functionallity exactly what i need (2 million points demo): http://www.mindscape.co.nz/demo/SilverlightElements/demopage.html#/ChartOverviewPage I will be grateful for any matherials, links or thoughts how to realize such functionallity.

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  • how to find maximum frequent item sets from large transactional data file

    - by ANIL MANE
    Hi, I have the input file contains large amount of transactions like Transaction ID Items T1 Bread, milk, coffee, juice T2 Juice, milk, coffee T3 Bread, juice T4 Coffee, milk T5 Bread, Milk T6 Coffee, Bread T7 Coffee, Bread, Juice T8 Bread, Milk, Juice T9 Milk, Bread, Coffee, T10 Bread T11 Milk T12 Milk, Coffee, Bread, Juice i want the occurrence of every unique item like Item Name Count Bread 9 Milk 8 Coffee 7 Juice 6 and from that i want an a fp-tree now by traversing this tree i want the maximal frequent itemsets as follows The basic idea of method is to dispose nodes in each “layer” from bottom to up. The concept of “layer” is different to the common concept of layer in a tree. Nodes in a “layer” mean the nodes correspond to the same item and be in a linked list from the “Head Table”. For nodes in a “layer” NBN method will be used to dispose the nodes from left to right along the linked list. To use NBN method, two extra fields will be added to each node in the ordered FP-Tree. The field tag of node N stores the information of whether N is maximal frequent itemset, and the field count’ stores the support count information in the nodes at left. In Figure, the first node to be disposed is “juice: 2”. If the min_sup is equal to or less than 2 then “bread, milk, coffee, juice” is a maximal frequent itemset. Firstly output juice:2 and set the field tag of “coffee:3” as “false” (the field tag of each node is “true” initially ). Next check whether the right four itemsets juice:1 be the subset of juice:2. If the itemset one node “juice:1” corresponding to is the subset of juice:2 set the field tag of the node “false”. In the following process when the field tag of the disposed node is FALSE we can omit the node after the same tagging. If the min_sup is more than 2 then check whether the right four juice:1 is the subset of juice:2. If the itemset one node “juice:1” corresponding to is the subset of juice:2 then set the field count’ of the node with the sum of the former count’ and 2 After all the nodes “juice” disposed ,begin to dispose the node “coffee:3”. Any suggestions or available source code, welcome. thanks in advance

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  • Has RFC2324 been implemented?

    - by anthony-arnold
    I know RFC2324 was an April Fools joke. However, it seems pretty well thought out, and after reading it I figured it wouldn't be out of the question to design an automated coffee machine that used this extension to HTTP. We programmers love to reference this RFC when arguing web standards ("418 I'm a Teapot lolz!") but the joke's kind of on us. Ubiquitous computing research assumes that network-connected coffee machines are probably going to be quite common in the future, along with Internet-connected fruit and just about everything else. Has anyone actually implemented a coffee machine that is controlled via HTCPCP? Not necessarily commercial, but hacked together in a garage, maybe? I'm not talking about just a web server that responds to HTCPCP requests; I mean a real coffee machine that actually makes coffee. I haven't seen an example of that.

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  • backbone.js Model.get() returns undefined, scope using coffeescript + coffee toaster?

    - by benipsen
    I'm writing an app using coffeescript with coffee toaster (an awesome NPM module for stitching) that builds my app.js file. Lots of my application classes and templates require info about the current user so I have an instance of class User (extends Backbone.Model) stored as a property of my main Application class (extends Backbone.Router). As part of the initialization routine I grab the user from the server (which takes care of authentication, roles, account switching etc.). Here's that coffeescript: @user = new models.User @user.fetch() console.log(@user) console.log(@user.get('email')) The first logging statement outputs the correct Backbone.Model attributes object in the console just as it should: User _changing: false _escapedAttributes: Object _pending: Object _previousAttributes: Object _silent: Object attributes: Object account: Object created_on: "1983-12-13 00:00:00" email: "[email protected]" icon: "0" id: "1" last_login: "2012-06-07 02:31:38" name: "Ben Ipsen" roles: Object __proto__: Object changed: Object cid: "c0" id: "1" __proto__: ctor app.js:228 However, the second returns undefined despite the model attributes clearly being there in the console when logged. And just to make things even more interesting, typing "window.app.user.get('email')" into the console manually returns the expected value of "[email protected]"... ? Just for reference, here's how the initialize method compiles into my app.js file: Application.prototype.initialize = function() { var isMobile; isMobile = navigator.userAgent.match(/(iPhone|iPod|iPad|Android|BlackBerry)/); this.helpers = new views.DOMHelpers().initialize().setup_viewport(isMobile); this.user = new models.User(); this.user.fetch(); console.log(this.user); console.log(this.user.get('email')); return this; }; I initialize the Application controller in my static HTML like so: jQuery(document).ready(function(){ window.app = new controllers.Application(); }); Suggestions please and thank you!

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  • O&rsquo;Reilly E-Book of the Day 15/Aug/2014 - Advanced Quantitative Finance with C++

    - by TATWORTH
    Originally posted on: http://geekswithblogs.net/TATWORTH/archive/2014/08/15/orsquoreilly-e-book-of-the-day-15aug2014---advanced-quantitative-finance.aspxToday’s half-price book of the Day offer from O’Reilly at http://shop.oreilly.com/product/9781782167228.do?code=MSDEAL is Advanced Quantitative Finance with C++. “This book will introduce you to the key mathematical models used to price financial derivatives, as well as the implementation of main numerical models used to solve them. In particular, equity, currency, interest rates, and credit derivatives are discussed. In the first part of the book, the main mathematical models used in the world of financial derivatives are discussed. Next, the numerical methods used to solve the mathematical models are presented. Finally, both the mathematical models and the numerical methods are used to solve some concrete problems in equity, forex, interest rate, and credit derivatives.”

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