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  • Error at lapack cgesv when matrix is not singular

    - by Jan Malec
    This is my first post. I usually ask classmates for help, but they have a lot of work now and I'm too desperate to figure this out on my own :). I am working on a project for school and I have come to a point where I need to solve a system of linear equations with complex numbers. I have decided to call lapack routine "cgesv" from c++. I use the c++ complex library to work with complex numbers. Problem is, when I call the routine, I get error code "2". From lapack documentation: INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. Therefore, the element U(2, 2) should be zero, but it is not. This is how I declare the function: void cgesv_( int* N, int* NRHS, std::complex* A, int* lda, int* ipiv, std::complex* B, int* ldb, int* INFO ); This is how I use it: int *IPIV = new int[NA]; int INFO, NRHS = 1; std::complex<double> *aMatrix = new std::complex<double>[NA*NA]; for(int i=0; i<NA; i++){ for(int j=0; j<NA; j++){ aMatrix[j*NA+i] = A[i][j]; } } cgesv_( &NA, &NRHS, aMatrix, &NA, IPIV, B, &NB, &INFO ); And this is how the matrix looks like: (1,-160.85) (0,0.000306796) (0,-0) (0,-0) (0,-0) (0,0.000306796) (1,-40.213) (0,0.000306796) (0,-0) (0,-0) (0,-0) (0,0.000306796) (1,-0.000613592) (0,0.000306796) (0,-0) (0,-0) (0,-0) (0,0.000306796) (1,-40.213) (0,0.000306796) (0,-0) (0,-0) (0,-0) (0,0.000306796) (1,-160.85) I had to split the matrix colums, otherwise it did not format correctly. My first suspicion was that complex is not parsed correctly, but I have used lapack functions with complex numbers before this way. Any ideas?

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  • What is the most efficient way to solve system of equations containing the digamma function?

    - by Neil G
    What is the most efficient way to solve system of equations involving the digamma function? I have a vector v and I want to solve for a vector w such that for all i: digamma(sum(w)) - digamma(w_i) = v_i and w_i 0 I found the gsl function gsl_sf_psi, which is the digamma function (calculated using some kind of series.) Is there an identity I can use to reduce the equations? Is my best bet to use a solver? I am using C++0x; which solver is easiest to use and fast?

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  • Runge-Kutta Method with adaptive step

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

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  • Create Chemistry Equations and Diagrams in Word

    - by Matthew Guay
    Microsoft Word is a great tool for formatting text, but what if you want to insert a chemistry formula or diagram?  Thanks to a new free add-in for Word, you can now insert high-quality chemistry formulas and diagrams directly from the Ribbon in Word. Microsoft’s new Education Labs has recently released the new Chemistry Add-in for Word 2007 and 2010.  This free download adds support for entering and editing chemistry symbols, diagrams, and formulas using the standard XML based Chemical Markup Language.  You can convert any chemical name, such as benzene, or formula, such as H2O, into a chemical diagram, standard name, or formula.  Whether you’re a professional chemist, just taking chemistry in school, or simply curious about the makeup of Citric Acid, this add-in is an exciting way to bring chemistry to your computer. This add-in works great on Word 2007 and 2010, including the 64 bit version of Word 2010.  Please note that the current version is still in beta, so only run it if you are comfortable running beta products. Getting Started Download the Chemistry add-in from Microsoft Education Labs (link below), and unzip the file.  Then, run the ChemistryAddinforWordBeta2.Setup.msi. It may inform you that you need to install the Visual Studio Tools for Office 3.0.  Simply click Yes to download these tools. This will open the download in your default browser.  Simply click run, or save and then run it when it is downloaded. Now, click next to install the Visual Studio Tools for Office as usual. When this is finished, run the ChemistryAddinforWordBeta2.Setup.msi again.  This time, you can easily install it with the default options. Once it’s finished installing, open Word to try out the Chemistry Add-in.  You will be asked if you want to install this customization, so click Install to enable it. Now you will have a new Chemistry tab in your Word ribbon.  Here’s the ribbon in Word 2010… And here it is in Word 2007.   Using the Chemistry Add-in It’s very easy to insert nice chemistry diagrams and formulas in Word with the Chemistry add-in.  You can quickly insert a premade diagram from the Chemistry Gallery: Or you can insert a formula from file.  Simply click “From File” and choose any Chemical Markup Language (.cml) formatted file to insert the chemical formula. You can also convert any chemical name to it’s chemical form.  Simply select the word, right-click, select “Convert to Chemistry Zone” and then click on its name. Now you can see the chemical form in the sidebar if you click the Chemistry Navigator button, and can choose to insert the diagram into the document.  Some chemicals will automatically convert to the diagram in the document, while others simply link to it in the sidebar.  Either way, you can display exactly what you want. You can also convert a chemical formula directly to it’s chemical diagram.  Here we entered H2O and converted it to Chemistry Zone: This directly converted it to the diagram directly in the document. You can click the Edit button on the top, and from there choose to either edit the 2D model of the chemical, or edit the labels. When you click Edit Labels, you may be asked which form you wish to display.  Here’s the options for potassium permanganate: You can then edit the names and formulas, and add or remove any you wish. If you choose to edit the chemical in 2D, you can even edit the individual atoms and change the chemical you’re diagramming.  This 2D editor has a lot of options, so you can get your chemical diagram to look just like you want. And, if you need any help or want to learn more about the Chemistry add-in and its features, simply click the help button in the Chemistry Ribbon.  This will open a Word document containing examples and explanations which can be helpful in mastering all the features of this add-in. All of this works perfectly, whether you’re running it in Word 2007 or 2010, 32 or 64 bit editions. Conclusion Whether you’re using chemistry formulas everyday or simply want to investigate a chemical makeup occasionally, this is a great way to do it with tools you already have on your computer.  It will also help make homework a bit easier if you’re struggling with it in high school or college. Links Download the Chemistry Add-in for Word Introducing Chemistry Add-in for Word – MSDN blogs Chemistry Markup Language – Wikipedia Similar Articles Productive Geek Tips Geek Reviews: Using Dia as a Free Replacement for Microsoft VisioEasily Summarize A Word 2007 DocumentCreate a Hyperlink in a Word 2007 Flow Chart and Hide Annoying ScreenTipsHow To Create and Publish Blog Posts in Word 2010 & 2007Using Word 2007 as a Blogging Tool TouchFreeze Alternative in AutoHotkey The Icy Undertow Desktop Windows Home Server – Backup to LAN The Clear & Clean Desktop Use This Bookmarklet to Easily Get Albums Use AutoHotkey to Assign a Hotkey to a Specific Window Latest Software Reviews Tinyhacker Random Tips Revo Uninstaller Pro Registry Mechanic 9 for Windows PC Tools Internet Security Suite 2010 PCmover Professional Windows 7 Easter Theme YoWindoW, a real time weather screensaver Optimize your computer the Microsoft way Stormpulse provides slick, real time weather data Geek Parents – Did you try Parental Controls in Windows 7? 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  • number several equations with only one number

    - by Tim
    Hi, How can I number several equations in a align environment using only one number? For example \begin{align} w^T x_i + b \geqslant 1-\xi_i \text{ if } y_i=1, \nonumber \\ w^T x_i + b \leqslant -1+\xi_i \text{ if } y_i=-1, \end{align} The numbering will appear next to the second equation. But it would be better if it appears between the lines of the two equations. In this case how to label this group of equations for later referring to? Thanks and regards!

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  • Computing complex math equations in python

    - by dassouki
    Are there any libraries or techniques that simplify computing equations ? Take the following two examples: F = B * { [ a * b * sumOf (A / B ''' for all i ''' ) ] / [ sumOf(c * d * j) ] } where: F = cost from i to j B, a, b, c, d, j are all vectors in the format [ [zone_i, zone_j, cost_of_i_to_j], [..]] This should produce a vector F [ [1,2, F_1_2], ..., [i,j, F_i_j] ] T_ij = [ P_i * A_i * F_i_j] / [ SumOf [ Aj * F_i_j ] // j = 1 to j = n ] where: n is the number of zones T = vector [ [1, 2, A_1_2, P_1_2], ..., [i, j, A_i_j, P_i_j] ] F = vector [1, 2, F_1_2], ..., [i, j, F_i_j] so P_i would be the sum of all P_i_j for all j and Aj would be sum of all P_j for all i I'm not sure what I'm looking for, but perhaps a parser for these equations or methods to deal with multiple multiplications and products between vectors? To calculate some of the factors, for example A_j, this is what i use from collections import defaultdict A_j_dict = defaultdict(float) for A_item in TG: A_j_dict[A_item[1]] += A_item[3] Although this works fine, I really feel that it is a brute force / hacking method and unmaintainable in the case we want to add more variables or parameters. Are there any math equation parsers you'd recommend? Side Note: These equations are used to model travel. Currently I use excel to solve a lot of these equations; and I find that process to be daunting. I'd rather move to python where it pulls the data directly from our database (postgres) and outputs the results into the database. All that is figured out. I'm just struggling with evaluating the equations themselves. Thanks :)

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  • matlab fit exp2

    - by HelloWorld
    I'm unsuccessfully looking for documentation of fit function using exp2 (sum of 2 exponents). How to operate the function is clear: [curve, gof] = fit(x, y,'exp2'); But since there are multiple ways to fit a sum of exponents I'm trying to find out what algorithm is used. Particularly what happens when I'm fitting one exponent (the raw data) with a bit of noise, how the exponents are spread. I've simulated several cases, and it seems that it "drops" all the weight on the second set of coefficients, but row data analysis often shows different behavior. Does anyone have suggestions of documentation?

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  • '0' inserted when cross-referencing numbered equations in MSWord 2007

    - by Jyotirmoy Bhattacharya
    I am inserting numbered equations using tables and multi-level lists as described in http://blogs.msdn.com/b/microsoft_office_word/archive/2006/10/20/equation-numbering.aspx I want to cross-reference the equations in my text. To do so I go to Insert-Cross reference and among the "Numbered Items" I pick the equation I wish to refer to. The problem is that if I pick the "Insert reference to" as "Paragraph number" a zero is always inserted into my text. The surprising thing is that the hyperlink in the cross-reference points to the correct equation. Also if I choose "Insert reference to" as "Page number" then the correct page numbers are inserted and they are correctly updated too.

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  • Is there a way to convert MS 2010 Equation to Object in MS Equation 3.0?

    - by Teodorescu
    I have a lot of equations (for faculty) written in MS Equation (button from right side) and saved it in .docx format. All good and the best until my professor told me that he has MS 2003 and I have to convert from docx to doc format and the equations must be editable. I don't have enough time to rewrite all the equations in MS Equation 3.0. Is there a way to convert from MS Equation to MS Equation 3.0 Object to be recognized and editable in Word 2003?

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  • How to solve non-linear equations using python

    - by stars83clouds
    I have the following code: #!/usr/bin/env python from scipy.optimize import fsolve import math h = 6.634e-27 k = 1.38e-16 freq1 = 88633.9360e6 freq2 = 88631.8473e6 freq3 = 88630.4157e6 def J(freq,T): return (h*freq/k)/(math.exp(h*freq/(k*T))-1) def equations(x,y,z,w,a,b,c,d): f1 = a*(J(freq1,y)-J(freq1,2.73))*(1-math.exp(-a*z))-(J(freq2,x)-J(freq2,2.73))*(1-math.exp(-z)) f2 = b*(J(freq3,w)-J(freq3,2.73))*(1-math.exp(-b*z))-(J(freq2,x)-J(freq2,2.73))*(1-math.exp(-z)) f3 = c*(J(freq3,w)-J(freq3,2.73))*(1-math.exp(-b*z))-(J(freq1,y)-J(freq1,2.73))*(1-math.exp(-a*z)) f4 = d*(J((freq3+freq1)/2,(y+w)/2)-J((freq3+freq1)/2,2.73))-(J(freq2,x)-J(freq2,2.73))*(1-math.exp(-z)) return (f1,f2,f3,f4) So, I have defined the equations in the above code. However, I now wish to solve the above set of equations using fsolve or other alternative non-linear numerical routine. I tried the following syntax but with no avail: x,y,z,w = fsolve(equations, (1,1,1,1)) I keep getting the error that "x" is not defined. I am executing all commands at the command-line, since I have no idea how to run a batch of commands as above automatically in python. I welcome any advice on how to solve this.

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  • C++ Numerical Recipes &ndash; A New Adventure!

    - by JoshReuben
    I am about to embark on a great journey – over the next 6 weeks I plan to read through C++ Numerical Recipes 3rd edition http://amzn.to/YtdpkS I'll be reading this with an eye to C++ AMP, thinking about implementing the suitable subset (non-recursive, additive, commutative) to run on the GPU. APIs supporting HPC, GPGPU or MapReduce are all useful – providing you have the ability to choose the correct algorithm to leverage on them. I really think this is the most fascinating area of programming – a lot more exciting than LOB CRUD !!! When you think about it , everything is a function – we categorize & we extrapolate. As abstractions get higher & less leaky, sooner or later information systems programming will become a non-programmer task – you will be using WYSIWYG designers to build: GUIs MVVM service mapping & virtualization workflows ORM Entity relations In the data source SharePoint / LightSwitch are not there yet, but every iteration gets closer. For information workers, managed code is a race to the bottom. As MS futures are a bit shaky right now, the provider agnostic nature & higher barriers of entry of both C++ & Numerical Analysis seem like a rational choice to me. Its also fascinating – stepping outside the box. This is not the first time I've delved into numerical analysis. 6 months ago I read Numerical methods with Applications, which can be found for free online: http://nm.mathforcollege.com/ 2 years ago I learned the .NET Extreme Optimization library www.extremeoptimization.com – not bad 2.5 years ago I read Schaums Numerical Analysis book http://amzn.to/V5yuLI - not an easy read, as topics jump back & forth across chapters: 3 years ago I read Practical Numerical Methods with C# http://amzn.to/V5yCL9 (which is a toy learning language for this kind of stuff) I also read through AI a Modern Approach 3rd edition END to END http://amzn.to/V5yQSp - this took me a few years but was the most rewarding experience. I'll post progress updates – see you on the other side !

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  • The Numerical ‘Magic’ of Cyclic Numbers

    - by Akemi Iwaya
    If you love crunching numbers or are just a fan of awesome number ‘tricks’ to impress your friends with, then you will definitely want to have a look at cyclic numbers. Dr Tony Padilla from the University of Nottingham shows how these awesome numbers work in Numberphile’s latest video. Cyclic Numbers – Numberphile [YouTube] Want to learn more about cyclic numbers? Then make sure to visit the Wikipedia page linked below! Cyclic number [Wikipedia]     

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  • How to apply numerical integration on a graph layout

    - by Cumatru
    I've done some basic 1 D integration, but i can't wrap my head around things and apply it to my graph layout. So, consider the picture below: if i drag the red node to the right, i'm forcing his position to my mouse position the other nodes will "follow" him, but how ? For Verlet, to compute the newPosition, i need the acceleration for every node and the currentPosition. That is what i don't understand. How to i compute the acceleration and the currentPosition ? The currentPosition will be the position of the RedNode ? If yes, doesn't that means that they will all overlap ? http://i.stack.imgur.com/NCKmO.jpg

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  • Accepting a numerical range in a function call

    - by dekpos
    I have encountered two ways of doing it: void foo(int from, int to); /* 'from' inclusive, 'to' exclusive */ void foo(int startIndex, int rangelength); Has one style historically been preferred over the other? If so, was it just a matter of convention or was it due to some deeper underlying reason? I'm currently programming in Java and noticed that the Arrays class uses the former style. The exclusivity of the to argument felt somewhat unintuitive to me, which led me to ask this question.

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  • tool for adding parentheses to equations?

    - by jedierikb
    Is there an online tool for adding parentheses to simple math equations? For example, a + b * c into a + (b * c) Those who paid more attention in math class might be able to tackle order of operations for huge equations in their head, but I could often use some help (and verification of my thinking). I often encounter other people's libraries having equations and functions I need for my code, and this would be kind of helpful for debugging and understanding. I was hoping Wolfram Alpha would do this, but the output is not easy to plug back into most programming languages e.g. a + (bc)

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  • solve mathematical equation with 1 unknown (equations are dynamically built)

    - by chris-gr
    Hi, I have to built dynamically equations like following: x + x/3 + (x/3)/4 + (x/3/4)/2 = 50 Now I would like to evaluate this equation and get x. The equation is built dynamically. x is the leaf node in a taxonomy, the other 3 nodes are the super concepts. The divisor represents the number of children of the child nodes. Is there a library that allows to build such equations dynamically and resolve x? Thanks, Chris

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  • What is the basic design idea behind the Scala for-loop implicit box/unboxing of numerical types?

    - by IODEV
    I'm trying to understand the behavior of Scala for-loop implicit box/unboxing of "numerical" types. Why does the two first fail but not the rest? 1) Fails: scala for (i:Long <- 0 to 10000000L) {} <console>:19: error: type mismatch;<br> found : Long(10000000L) required: Int for (i:Long <- 0 to 10000000L) {} ^ 2 Fails: scala for (i <- 0 to 10000000L) {} <console>:19: error: type mismatch; found : Long(10000000L) required: Int for (i <- 0 to 10000000L) {} ^ 3) Works: scala for (i:Long <- 0L to 10000000L) {} 4) Works: scala for (i <- 0L to 10000000L) {}

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  • Solving Diophantine Equations Using Python

    - by HARSHITH
    In mathematics, a Diophantine equation (named for Diophantus of Alexandria, a third century Greek mathematician) is a polynomial equation where the variables can only take on integer values. Although you may not realize it, you have seen Diophantine equations before: one of the most famous Diophantine equations is: We are not certain that McDonald's knows about Diophantine equations (actually we doubt that they do), but they use them! McDonald's sells Chicken McNuggets in packages of 6, 9 or 20 McNuggets. Thus, it is possible, for example, to buy exactly 15 McNuggets (with one package of 6 and a second package of 9), but it is not possible to buy exactly 16 nuggets, since no non- negative integer combination of 6's, 9's and 20's adds up to 16. To determine if it is possible to buy exactly n McNuggets, one has to solve a Diophantine equation: find non-negative integer values of a, b, and c, such that 6a + 9b + 20c = n. Write an iterative program that finds the largest number of McNuggets that cannot be bought in exact quantity. Your program should print the answer in the following format (where the correct number is provided in place of n): "Largest number of McNuggets that cannot be bought in exact quantity: n"

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  • Efficient process SQL Server and numerical methods library

    - by darkcminor
    Is there a way to comunicate a numeric method library, that can exploit all .net's (numerical methods called by .net that does SQL Server things) habilities?, What library do you recomend, maybe using MATLAB, R? How to comunicate SQL Server and .net with such library or libraries? Do you have an example? What steps must be followed to make the link between numerical libraries, .net and SQL Server

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  • convert Arabic numerical to English

    - by hamitay
    i am looking for a way to convert the Arabic numerical string "??????????" to an English numerical string "0123456789" Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click dim Anum as string ="??????????" dim Enum as string =get_egnlishNum(Anum) End Sub private function get_egnlishNum(byval _Anum as string) as string '' converting code end function

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  • Importing long numerical identifiers into Excel

    - by Niels Basjes
    I have some data in a database that uses ids that have the form of 16 digit numbers. In some situations i need to export the data in such a way that it can be manipulated in excel. So i export the data into a file and import it into excel. I've tried several file formats and I'm stuck. The problem I'm facing is that when reading a file into excel that has a cell that looks like a number then excel treats it as a number. The catch is that (as far as i can tell) all numerical values in excel are double precision floating point which have a precision of less than 16 digits. So my ids are changed: very often the last digit its changed to a 0. So far I've only been able to convince excel to keep the Id unchanged by breaking it myself: by adding a letter or symbol to the Id. This however means that in order to use the value again it must be "unbroken". Is there a way to create a file where i can specify that excel must treat the value as a text without changing the value? Or its there a way to let excel treat the value as a long (64bit integer)?

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  • How to strike out inside LaTeX equations?

    - by Aamir
    Please see the snippet below and tell me how can I achieve the same strike-out effect as in the main text. I am using the version of LaTeX from the latest Ubuntu repositories. \documentclass{article} \usepackage{ulem} \begin{document} The sout tag works perfect in the \sout{main text area} but not inside the equations. $$ list = [1, \sout{2}, 3, \sout{4}, 5, \sout{6}, 7, \sout{8}, 9, \sout{10}] $$ Any clue? \end{document} Here is LaTeX output

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