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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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  • 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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  • 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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  • Add Excel column without breaking equation

    - by CRAIG
    I have completed a very complex Excel spreadsheet with a lot of equations, except ... I forgot to include September I have Jan through Dec, all the months, except the calculations for September. Of course all the equations are currently perfect for the data that's here. How do I add a whole new column without ruining the previous equations? PS: tomorrow is my holidays and I have to go to work to finish this table, so bad

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  • How to replace all images in Libreoffice with their description

    - by user30131
    I have a very long document containing lots of svg images created using the extension TexMaths. This extension uses the latex installation to create svg image of the inputted equation (or set of equations). The latex code for each equation (or set of equations) is embedded in the image as part of its Description. Such a Description can be accessed by right clicking the svg image and choosing the option Description. I want to replace all the svg images using a suitable macro, by the embedded descriptions. e.g. from The Einstein's famous equation, [svg embedded equation : E = mc 2], tells us that mass can be converted to energy and vice-versa. To The Einstein's famous equation, E = mc^2, tells us that mass can be converted to energy and vice-versa. This will allow me to convert by hand the odt file containing numerous TexMaths equations to LaTeX.

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  • Greasemonkey script for inserting math in gmail

    - by Elazar Leibovich
    I wish an easy way to communicate mathematical equations with gmail. There's a javascript script called AsciiMath, which should translate Tex-like equations into standard mathML. I thought that it would be nice to use this script with GM. I thought that before sending the email, this script would convert all the TeX-like equations in your email to MathML. Thus the reader which is using FF (or IE with MathPlayer installed) would be able to easily read those equations. Ideally, I wish to somehow keep the original TeX-like equations in a plain-text message, so that it would be readable by plain text email clients, such as mutt. Obviously the weakest link here is the client software, which most likely doesn't support MathML. Still if my correspondent is using Firefox and some kind of webmail (which is pretty reasonable) - it should work. My question is, is it possible? Did anyone do that? Do you see any technical problems with this approach (gmail filtering the MathML, client not parsing it correctly etc.)? Any smarter ideas?

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  • Logic error for Gauss elimination

    - by iwanttoprogram
    Logic error problem with the Gaussian Elimination code...This code was from my Numerical Methods text in 1990's. The code is typed in from the book- not producing correct output... Sample Run: SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS USING GAUSSIAN ELIMINATION This program uses Gaussian Elimination to solve the system Ax = B, where A is the matrix of known coefficients, B is the vector of known constants and x is the column matrix of the unknowns. Number of equations: 3 Enter elements of matrix [A] A(1,1) = 0 A(1,2) = -6 A(1,3) = 9 A(2,1) = 7 A(2,2) = 0 A(2,3) = -5 A(3,1) = 5 A(3,2) = -8 A(3,3) = 6 Enter elements of [b] vector B(1) = -3 B(2) = 3 B(3) = -4 SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS The solution is x(1) = 0.000000 x(2) = -1.#IND00 x(3) = -1.#IND00 Determinant = -1.#IND00 Press any key to continue . . . The code as copied from the text... //Modified Code from C Numerical Methods Text- June 2009 #include <stdio.h> #include <math.h> #define MAXSIZE 20 //function prototype int gauss (double a[][MAXSIZE], double b[], int n, double *det); int main(void) { double a[MAXSIZE][MAXSIZE], b[MAXSIZE], det; int i, j, n, retval; printf("\n \t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS"); printf("\n \t USING GAUSSIAN ELIMINATION \n"); printf("\n This program uses Gaussian Elimination to solve the"); printf("\n system Ax = B, where A is the matrix of known"); printf("\n coefficients, B is the vector of known constants"); printf("\n and x is the column matrix of the unknowns."); //get number of equations n = 0; while(n <= 0 || n > MAXSIZE) { printf("\n Number of equations: "); scanf ("%d", &n); } //read matrix A printf("\n Enter elements of matrix [A]\n"); for (i = 0; i < n; i++) for (j = 0; j < n; j++) { printf(" A(%d,%d) = ", i + 1, j + 1); scanf("%lf", &a[i][j]); } //read {B} vector printf("\n Enter elements of [b] vector\n"); for (i = 0; i < n; i++) { printf(" B(%d) = ", i + 1); scanf("%lf", &b[i]); } //call Gauss elimination function retval = gauss(a, b, n, &det); //print results if (retval == 0) { printf("\n\t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS\n"); printf("\n\t The solution is"); for (i = 0; i < n; i++) printf("\n \t x(%d) = %lf", i + 1, b[i]); printf("\n \t Determinant = %lf \n", det); } else printf("\n \t SINGULAR MATRIX \n"); return 0; } /* Solves the system of equations [A]{x} = {B} using */ /* the Gaussian elimination method with partial pivoting. */ /* Parameters: */ /* n - number of equations */ /* a[n][n] - coefficient matrix */ /* b[n] - right-hand side vector */ /* *det - determinant of [A] */ int gauss (double a[][MAXSIZE], double b[], int n, double *det) { double tol, temp, mult; int npivot, i, j, l, k, flag; //initialization *det = 1.0; tol = 1e-30; //initial tolerance value npivot = 0; //mult = 0; //forward elimination for (k = 0; k < n; k++) { //search for max coefficient in pivot row- a[k][k] pivot element for (i = k + 1; i < n; i++) { if (fabs(a[i][k]) > fabs(a[k][k])) { //interchange row with maxium element with pivot row npivot++; for (l = 0; l < n; l++) { temp = a[i][l]; a[i][l] = a[k][l]; a[k][l] = temp; } temp = b[i]; b[i] = b[k]; b[k] = temp; } } //test for singularity if (fabs(a[k][k]) < tol) { //matrix is singular- terminate flag = 1; return flag; } //compute determinant- the product of the pivot elements *det = *det * a[k][k]; //eliminate the coefficients of X(I) for (i = k; i < n; i++) { mult = a[i][k] / a[k][k]; b[i] = b[i] - b[k] * mult; //compute constants for (j = k; j < n; j++) //compute coefficients a[i][j] = a[i][j] - a[k][j] * mult; } } //adjust the sign of the determinant if(npivot % 2 == 1) *det = *det * (-1.0); //backsubstitution b[n] = b[n] / a[n][n]; for(i = n - 1; i > 1; i--) { for(j = n; j > i + 1; j--) b[i] = b[i] - a[i][j] * b[j]; b[i] = b[i] / a[i - 1][i]; } flag = 0; return flag; } The solution should be: 1.058824, 1.823529, 0.882353 with det as -102.000000 Any insight is appreciated...

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  • excel 2010 format and input issue

    - by Craig Gunn
    I have completed a very complex Excel spreadsheet with a lot of equations, except ... I forgot to include September I have Jan through Dec, all the months, except the calculations for September. Of course all the equations are currently perfect for the data that's here. How do I add a whole new column without ruining the previous equations? PS: tomorrow is my holidays and I have to go to work to finish this table, so bad. would really appreciate some kind expertise :) cheers craig.

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  • Pandoc: Output two sumation signs in equal height in Word 2010

    - by Andy
    I need to output some complex equations in Word 2010 (docx). To do so I write most of the equations in tex and use pandoc to translate them as Word formulas. However I have a problem with the following tex equation: \sum_{m=1}^\infty\sum_{n=1}^\infty In Word the resulting two summation signs are not of the same size but the latter is smaler than the first one. Is there any workaround to solve this? I would deeply appreciate any help. Thank you Andy

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  • Mapping A Sphere To A Cube

    - by petrocket
    There is a special way of mapping a cube to a sphere described here: http://mathproofs.blogspot.com/2005/07/mapping-cube-to-sphere.html It is not your basic "normalize the point and your done" approach and gives a much more evenly spaced mapping. I've tried to do the inverse of the mapping going from sphere coords to cube coords and have been unable to come up the working equations. It's a rather complex system of equations with lots of square roots. Any math geniuses want to take a crack at it? Here's the equations in c++ code: sx = x * sqrtf(1.0f - y * y * 0.5f - z * z * 0.5f + y * y * z * z / 3.0f); sy = y * sqrtf(1.0f - z * z * 0.5f - x * x * 0.5f + z * z * x * x / 3.0f); sz = z * sqrtf(1.0f - x * x * 0.5f - y * y * 0.5f + x * x * y * y / 3.0f); sx,sy,sz are the sphere coords and x,y,z are the cube coords.

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  • Greek Letters rendered incorrectly in LibreOffice

    - by Matheus de Araújo
    Using an old archive that I have (with Maxwell's equations), the Greek letters display as squares. I tried to change something in the alphabet but even the fonts don't have any Greek letters (they appear like squares too), both Greek and iGreek letters packages. Sounds like a package that's not installed, or corrupted. I still re-downloaded and reinstalled LibreOffice. I don't know what I have to install. The equations look fine in OpenOffice.org (I made the file with it). What should I do?

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  • LibreOffice Math problem with greek letters

    - by Matheus de Araújo
    I've a problem with my LibreOffice. Using an old archive that I have (with the Maxwell's equations), the greek letters are like squares. I tried to change something in the alphabet but even the font don't have any greek letters (they appear like squares too), both Greek and iGreek letters package. Sounds like a packet that isn't installed or corrupted, but I still redownloaded and reinstalled the LO and I don't know whose I have to install. With the OO my equations worked well (I made the file with it). What am I supposed to do?

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  • Extreme Optimization Numerical Libraries for .NET – Part 1 of n

    - by JoshReuben
    While many of my colleagues are fascinated in constructing the ultimate ViewModel or ServiceBus, I feel that this kind of plumbing code is re-invented far too many times – at some point in the near future, it will be out of the box standard infra. How many times have you been to a customer site and built a different variation of the same kind of code frameworks? How many times can you abstract Prism or reliable and discoverable WCF communication? As the bar is raised for whats bundled with the framework and more tasks become declarative, automated and configurable, Information Systems will expose a higher level of abstraction, forcing software engineers to focus on more advanced computer science and algorithmic tasks. I've spent the better half of the past decade building skills in .NET and expanding my mathematical horizons by working through the Schaums guides. In this series I am going to examine how these skillsets come together in the implementation provided by ExtremeOptimization. Download the trial version here: http://www.extremeoptimization.com/downloads.aspx Overview The library implements a set of algorithms for: linear algebra, complex numbers, numerical integration and differentiation, solving equations, optimization, random numbers, regression, ANOVA, statistical distributions, hypothesis tests. EONumLib combines three libraries in one - organized in a consistent namespace hierarchy. Mathematics Library - Extreme.Mathematics namespace Vector and Matrix Library - Extreme.Mathematics.LinearAlgebra namespace Statistics Library - Extreme.Statistics namespace System Requirements -.NET framework 4.0  Mathematics Library The classes are organized into the following namespace hierarchy: Extreme.Mathematics – common data types, exception types, and delegates. Extreme.Mathematics.Calculus - numerical integration and differentiation of functions. Extreme.Mathematics.Curves - points, lines and curves, including polynomials and Chebyshev approximations. curve fitting and interpolation. Extreme.Mathematics.Generic - generic arithmetic & linear algebra. Extreme.Mathematics.EquationSolvers - root finding algorithms. Extreme.Mathematics.LinearAlgebra - vectors , matrices , matrix decompositions, solvers for simultaneous linear equations and least squares. Extreme.Mathematics.Optimization – multi-d function optimization + linear programming. Extreme.Mathematics.SignalProcessing - one and two-dimensional discrete Fourier transforms. Extreme.Mathematics.SpecialFunctions

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  • Logarithmic spacing of FFT bins

    - by Mykel Stone
    I'm trying to do the examples within the GameDev.net Beat Detection article ( http://archive.gamedev.net/archive/reference/programming/features/beatdetection/index.html ) I have no issue with performing a FFT and getting the frequency data and doing most of the article. I'm running into trouble though in the section 2.B, Enhancements and beat decision factors. in this section the author gives 3 equations numbered R10-R12 to be used to determine how many bins go into each subband: R10 - Linear increase of the width of the subband with its index R11 - We can choose for example the width of the first subband R12 - The sum of all the widths must not exceed 1024 He says the following in the article: "Once you have equations (R11) and (R12) it is fairly easy to extract 'a' and 'b', and thus to find the law of the 'wi'. This calculus of 'a' and 'b' must be made manually and 'a' and 'b' defined as constants in the source; indeed they do not vary during the song." However, I cannot seem to understand how these values are calculated...I'm probably missing something simple, but learning fourier analysis in a couple of weeks has left me Decimated-in-Mind and I cannot seem to see it.

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  • Logarithmic spacing of FFT subbands

    - by Mykel Stone
    I'm trying to do the examples within the GameDev.net Beat Detection article ( http://archive.gamedev.net/archive/reference/programming/features/beatdetection/index.html ) I have no issue with performing a FFT and getting the frequency data and doing most of the article. I'm running into trouble though in the section 2.B, Enhancements and beat decision factors. in this section the author gives 3 equations numbered R10-R12 to be used to determine how many bins go into each subband: R10 - Linear increase of the width of the subband with its index R11 - We can choose for example the width of the first subband R12 - The sum of all the widths must not exceed 1024 He says the following in the article: "Once you have equations (R11) and (R12) it is fairly easy to extract 'a' and 'b', and thus to find the law of the 'wi'. This calculus of 'a' and 'b' must be made manually and 'a' and 'b' defined as constants in the source; indeed they do not vary during the song." However, I cannot seem to understand how these values are calculated...I'm probably missing something simple, but learning fourier analysis in a couple of weeks has left me Decimated-in-Mind and I cannot seem to see it.

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  • Parsing mathematical experssions with two values that have parenthesis and minus signs

    - by user45921
    I'm trying to parse equations like these which only has two values or the square root of a certain value from a text file: 100+100 -100-100 -(100)+(-100) sqrt(100) by the minues signs, parenthesis and the operator symbol in the middle and the square root, and I have no idea how to start off... I've got the file part done and the simple calculation parts except that I couldnt get my program to solve the equations in the above. #include <stdio.h> #include <string.h> #include <stdlib.h> #include <math.h> main(){ FILE *fp; char buff[255], sym,sym2,del1,del2,del3,del4; double num1, num2; int ret; fp = fopen("input.txt","r"); while(fgets(buff,sizeof(buff),fp)!=NULL){ char *tok = buff; sscanf(tok,"%lf%c%lf",&num1,&sym,&num2); switch(sym){ case '+': printf("%lf\n", num1+num2); break; case '-': printf("%lf\n", num1-num2); break; case '*': printf("%lf\n", num1*num2); break; case '/': printf("%lf\n", num1/num2); break; default: printf("The input value is not correct\n"); break; } } fclose(fp); } that is what have I written for the other basic operations without parenthesis and the minus sign for the second value and it works great for the simple ones. I'm using a switch method to calculate the add, sub, mul and divide but I'm not sure how to properly use the sscanf function (if I am not using it properly) or if there is another way using a function like strtok to properly parse the parenthesis and the minus signs. Any kind help?

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  • 2D isometric picking

    - by Bikonja
    I'm trying to implement picking in my isometric 2D game, however, I am failing. First of all, I've searched for a solution and came to several, different equations and even a solution using matrices. I tried implementing every single one, but none of them seem to work for me. The idea is that I have an array of tiles, with each tile having it's x and y coordinates specified (in this simplified example it's by it's position in the array). I'm thinking that the tile (0, 0) should be on the left, (max, 0) on top, (0, max) on the bottom and (max, max) on the right. I came up with this loop for drawing, which googling seems to have verified as the correct solution, as has the rendered scene (ofcourse, it could still be wrong, also, forgive the messy names and stuff, it's just a WIP proof of concept code) // Draw code int col = 0; int row = 0; for (int i = 0; i < nrOfTiles; ++i) { // XOffset and YOffset are currently hardcoded values, but will represent camera offset combined with HUD offset Point tile = IsoToScreen(col, row, TileWidth / 2, TileHeight / 2, XOffset, YOffset); int x = tile.X; int y = tile.Y; spriteBatch.Draw(_tiles[i], new Rectangle(tile.X, tile.Y, TileWidth, TileHeight), Color.White); col++; if (col >= Columns) // Columns is the number of tiles in a single row { col = 0; row++; } } // Get selection overlay location (removed check if selection exists for simplicity sake) Point tile = IsoToScreen(_selectedTile.X, _selectedTile.Y, TileWidth / 2, TileHeight / 2, XOffset, YOffset); spriteBatch.Draw(_selectionTexture, new Rectangle(tile.X, tile.Y, TileWidth, TileHeight), Color.White); // End of draw code public Point IsoToScreen(int isoX, int isoY, int widthHalf, int heightHalf, int xOffset, int yOffset) { Point newPoint = new Point(); newPoint.X = widthHalf * (isoX + isoY) + xOffset; newPoint.Y = heightHalf * (-isoX + isoY) + yOffset; return newPoint; } This code draws the tiles correctly. Now I wanted to do picking to select the tiles. For this, I tried coming up with equations of my own (including reversing the drawing equation) and I tried multiple solutions I found on the internet and none of these solutions worked. Trying out lots of solutions, I came upon one that didn't work, but it seemed like an axis was just inverted. I fiddled around with the equations and somehow managed to get it to actually work (but have no idea why it works), but while it's close, it still doesn't work. I'm not really sure how to describe the behaviour, but it changes the selection at wrong places, while being fairly close (sometimes spot on, sometimes a tile off, I believe never more off than the adjacent tile). This is the code I have for getting which tile coordinates are selected: public Point? ScreenToIso(int screenX, int screenY, int tileHeight, int offsetX, int offsetY) { Point? newPoint = null; int nX = -1; int nY = -1; int tX = screenX - offsetX; int tY = screenY - offsetY; nX = -(tY - tX / 2) / tileHeight; nY = (tY + tX / 2) / tileHeight; newPoint = new Point(nX, nY); return newPoint; } I have no idea why this code is so close, especially considering it doesn't even use the tile width and all my attempts to write an equation myself or use a solution I googled failed. Also, I don't think this code accounts for the area outside the "tile" (the transparent part of the tile image), for which I intend to add a color map, but even if that's true, it's not the problem as the selection sometimes switches on approx 25% or 75% of width or height. I'm thinking I've stumbled upon a wrong path and need to backtrack, but at this point, I'm not sure what to do so I hope someone can shed some light on my error or point me to the right path. It may be worth mentioning that my goal is to not only pick the tile. Each main tile will be divided into 5x5 smaller tiles which won't be drawn seperately from the whole main tile, but they will need to be picked out. I think a color map of a main tile with different colors for different coordinates within the main tile should take care of that though, which would fall within using a color map for the main tile (for the transparent parts of the tile, meaning parts that possibly belong to other tiles).

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  • Creating an equation in a word 2003 document using a marco (or through the API)

    - by Sambatyon
    I think the title is fully descriptive. Anyway, I need to generate a word document from my delphi application. It needs to choose from one of four different equations (with some specific parameters for each document). So far I have manage to create the whole document programmatically except the equation. Is it possible to create equations programmatically? if so, where is de API documentation from MS? if not, which solution can be used?

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  • Diophantine Equation [closed]

    - by ANIL
    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: X^n+Y^n=Z^n 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. Problem 1 Show that it is possible to buy exactly 50, 51, 52, 53, 54, and 55 McNuggets, by finding solutions to the Diophantine equation. You can solve this in your head, using paper and pencil, or writing a program. However you chose to solve this problem, list the combinations of 6, 9 and 20 packs of McNuggets you need to buy in order to get each of the exact amounts. Given that it is possible to buy sets of 50, 51, 52, 53, 54 or 55 McNuggets by combinations of 6, 9 and 20 packs, show that it is possible to buy 56, 57,..., 65 McNuggets. In other words, show how, given solutions for 50-55, one can derive solutions for 56-65. Problem 2 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" Hints: Hypothesize possible instances of numbers of McNuggets that cannot be purchased exactly, starting with 1 For each possible instance, called n, a. Test if there exists non-negative integers a, b, and c, such that 6a+9b+20c = n. (This can be done by looking at all feasible combinations of a, b, and c) b. If not, n cannot be bought in exact quantity, save n When you have found six consecutive values of n that in fact pass the test of having an exact solution, the last answer that was saved (not the last value of n that had a solution) is the correct answer, since you know by the theorem that any amount larger can also be bought in exact quantity

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  • Creating an Equation Editor 3.0 equation in a Word 2003 document using a marco (or through the API)

    - by Sambatyon
    I think the title is fully descriptive now. Anyway, I need to generate a word document from my delphi application. It needs to choose from one of four different equations (with some specific parameters for each document). So far I have manage to create the whole document programmatically except the equation. Is it possible to create equations programmatically? if so, where is de API documentation from MS? if not, which solution can be used?

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  • Efficient algorithm to generate all solutions of a linear diophantine equation with ai=1

    - by Ben
    I am trying to generate all the solutions for the following equations for a given H. With H=4 : 1) ALL solutions for x_1 + x_2 + x_3 + x_4 =4 2) ALL solutions for x_1 + x_2 + x_3 = 4 3) ALL solutions for x_1 + x_2 = 4 4) ALL solutions for x_1 =4 For my problem, there are always 4 equations to solve (independently from the others). There are a total of 2^(H-1) solutions. For the previous one, here are the solutions : 1) 1 1 1 1 2) 1 1 2 and 1 2 1 and 2 1 1 3) 1 3 and 3 1 and 2 2 4) 4 Here is an R algorithm which solve the problem. library(gtools) H<-4 solutions<-NULL for(i in seq(H)) { res<-permutations(H-i+1,i,repeats.allowed=T) resum<-apply(res,1,sum) id<-which(resum==H) print(paste("solutions with ",i," variables",sep="")) print(res[id,]) } However, this algorithm makes more calculations than needed. I am sure it is possible to go faster. By that, I mean not generating the permutations for which the sums is H Any idea of a better algorithm for a given H ?

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