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• Excel 2007: plot data points not on an axis/ force linear x-incrementation without altering integrity of non-linear data

  - by Ennapode

  In Excel, how does one go about plotting points that don't have an x component that is an x-axis label? For example, in my graph, the x-components are derived from the cosine function and aren't linear, but Excel is displaying them as if .0016 to .0062 to .0135 is an equal incrementation. How would I change this so that the x-axis has an even incrementation without altering the integrity of the points themselves? In other words, how do I plot a point with an x component independent from the x-axis label?

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• Bilinear interpolation - DirectX vs. GDI+

  - by holtavolt

  I have a C# app for which I've written GDI+ code that uses Bitmap/TextureBrush rendering to present 2D images, which can have various image processing functions applied. This code is a new path in an application that mimics existing DX9 code, and they share a common library to perform all vector and matrix (e.g. ViewToWorld/WorldToView) operations. My test bed consists of DX9 output images that I compare against the output of the new GDI+ code. A simple test case that renders to a viewport that matches the Bitmap dimensions (i.e. no zoom or pan) does match pixel-perfect (no binary diff) - but as soon as the image is zoomed up (magnified), I get very minor differences in 5-10% of the pixels. The magnitude of the difference is 1 (occasionally 2)/256. I suspect this is due to interpolation differences. Question: For a DX9 ortho projection (and identity world space), with a camera perpendicular and centered on a textured quad, is it reasonable to expect DirectX.Direct3D.TextureFilter.Linear to generate identical output to a GDI+ TextureBrush filled rectangle/polygon when using the System.Drawing.Drawing2D.InterpolationMode.Bilinear setting? For this (magnification) case, the DX9 code is using this (MinFilter,MipFilter set similarly): Device.SetSamplerState(0, SamplerStageStates.MagFilter, (int)TextureFilter.Linear); and the GDI+ path is using: g.InterpolationMode = InterpolationMode.Bilinear; I thought that "Bilinear Interpolation" was a fairly specific filter definition, but then I noticed that there is another option in GDI+ for "HighQualityBilinear" (which I've tried, with no difference - which makes sense given the description of "added prefiltering for shrinking") Followup Question: Is it reasonable to expect pixel-perfect output matching between DirectX and GDI+ (assuming all external coordinates passed in are equal)? If not, why not? Finally, there are a number of other APIs I could be using (Direct2D, WPF, GDI, etc.) - and this question generally applies to comparing the output of "equivalent" bilinear interpolated output images across any two of these. Thanks!

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• Objective-C 2D Interpolation

  - by Brett

  Has anyone come across an Objective-C equivalent to the MATLAB function interp2()? ...a 2D interpolation. Cheers, Brett

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• Interpolate air drag for my game?

  - by Valentin Krummenacher

  So I have a little game which works with small steps, however those steps vary in time, so for example I sometimes have 10 Steps/second and then I have 20 Steps/second. This changes automatically depending on how many steps the user's computer can take. To avoid inaccurate positioning of the game's player object I use y=v0*dt+g*dt^2/2 to determine my objects y-position, where dt is the time since the last step, v0 is the velocity of my object in the beginning of my step and g is the gravity. To calculate the velocity in the end of a step I use v=v0+g*dt what also gives me correct results, independent of whether I use 2 steps with a dt of for example 20ms or one step with a dt of 40ms. Now I would like to introduce air drag. For simplicity's sake I use a=k*v^2 where a is the air drag's acceleration (I am aware that it would usually result in a force, but since I assume 1kg for my object's mass the force is the same as the resulting acceleration), k is a constant (in this case I'm using 0.001) and v is the speed. Now in an infinitely small time interval a is k multiplied by the velocity in this small time interval powered by 2. The problem is that v in the next time interval would depend on the drag of the last which again depends on the v of the last interval and so on... In other words: If I use a=k*v^2 I get different results for my position/velocity when I use 2 steps of 20ms than when I use one step of 40ms. I used to have this problem for my position too, but adding +g*dt^2/2 to the formula for my position fixed the problem since it takes into account that the position depends on the velocity which changes slightly in every infinitely small time interval. Does something like that exist for air drag too? And no, I dont mean anything like Adding air drag to a golf ball trajectory equation or similar, for that kind of method only gives correct results when all my steps are the same. (I hope you can understand my intermediate english, it's not my main language so I would like to say sorry for all the silly mistakes I might have made in my question)

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• Computing pixel's screen position in a vertex shader: right or wrong?

  - by cubrman

  I am building a deferred rendering engine and I have a question. The article I took the sample code from suggested computing screen position of the pixel as follows: VertexShaderFunction() { ... output.Position = mul(worldViewProj, input.Position); output.ScreenPosition = output.Position; } PixelShaderFunction() { input.ScreenPosition.xy /= input.ScreenPosition.w; float2 TexCoord = 0.5f * (float2(input.ScreenPosition.x,-input.ScreenPosition.y) + 1); ... } The question is what if I compute the position in the vertex shader (which should optimize the performance as VSF is launched significantly less number of times than PSF) would I get the per-vertex lighting insted. Here is how I want to do this: VertexShaderFunction() { ... output.Position = mul(worldViewProj, input.Position); output.ScreenPosition.xy = output.Position / output.Position.w; } PixelShaderFunction() { float2 TexCoord = 0.5f * (float2(input.ScreenPosition.x,-input.ScreenPosition.y) + 1); ... } What exactly happens with the data I pass from VS to PS? How exactly is it interpolated? Will it give me the right per-pixel result in this case? I tried launching the game both ways and saw no visual difference. Is my assumption right? Thanks. P.S. I am optimizing the point light shader, so I actually pass a sphere geometry into the VS.

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• -moz-linear-gradient

  - by bah

  Hi, Could someone explain to me what this portion of code means? repeat scroll 0 0 #F6F6F6; I have googled a lot and only found syntax to this part -moz-linear-gradient(center top , #FFFFFF, #EFEFEF) My code: background: -moz-linear-gradient(center top , #FFFFFF, #EFEFEF) repeat scroll 0 0 #F6F6F6; Thanks!

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• Interpolating Matrices

  - by sebf

  Hello, Apologies if I am missing something very obvious (likely!) but is there anything wrong with interpolating between two matrices by: float d = (float)(targetTime.Ticks - keyframe_start.ticks) / (float)(keyframe_end.ticks - keyframe_start.ticks); return ((keyframe_start.Transform * (1 - d)) + (keyframe_end.Transform * d)); As in my app, when I try an use this to interpolate between two keyframes, the model begins to 'shrink' - the severity based on how far between the two keyframes the target time is; its worst when the transform split is ~50/50.

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• bitmap interpolation c#

  - by Raghav

  Grid size : 160*160 No of row* columns = 16*16 I have created a bitmap for this. Each cell of the grid is filled with different colors. I need to perform color interpolation.

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• Linear Performance Scalability with HP San Solutions

  - by Berzemus

  Hi all, I need a San Solution with linear scalability in size as well as in performance. From what I know, with a Modular Smart Array solution such as the P2000/MSA-class solutions from HP, even with a dual controller initial node, I can only increase the size of it, as added nodes come controller-less, so overall performance tends to decrease. On the other hand, the P4000 (lefthand) family of solutions has each of it's nodes have it's own controller, and so when a node is added, storage capacity as well as performance increase. Am I right in all that I say, and is the P4000 the only solution, or have I forgotten something ?

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• Server-side Input

  - by Thomas

  Currently in my game, the client is nothing but a renderer. When input state is changed, the client sends a packet to the server and moves the player as if it were processing the input, but the server has the final say on the position. This generally works really well, except for one big problem: falling off edges. Basically, if a player is walking towards an edge, say a cliff, and stops right before going off the edge, sometimes a second later, he'll be teleported off of the edge. This is because the "I stopped pressing W" packet is sent after the server processes the information. Here's a lag diagram to help you understand what I mean: http://i.imgur.com/Prr8K.png I could just send a "W Pressed" packet each frame for the server to process, but that would seem to be a bandwidth-costly solution. Any help is appreciated!

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• Extrapolation breaks collision detection

  - by user22241

  Before applying extrapolation to my sprite's movement, my collision worked perfectly. However, after applying extrapolation to my sprite's movement (to smooth things out), the collision no longer works. This is how things worked before extrapolation: However, after I implement my extrapolation, the collision routine breaks. I am assuming this is because it is acting upon the new coordinate that has been produced by the extrapolation routine (which is situated in my render call ). After I apply my extrapolation How to correct this behaviour? I've tried puting an extra collision check just after extrapolation - this does seem to clear up a lot of the problems but I've ruled this out because putting logic into my rendering is out of the question. I've also tried making a copy of the spritesX position, extrapolating that and drawing using that rather than the original, thus leaving the original intact for the logic to pick up on - this seems a better option, but it still produces some weird effects when colliding with walls. I'm pretty sure this also isn't the correct way to deal with this. I've found a couple of similar questions on here but the answers haven't helped me. This is my extrapolation code: public void onDrawFrame(GL10 gl) { //Set/Re-set loop back to 0 to start counting again loops=0; while(System.currentTimeMillis() > nextGameTick && loops < maxFrameskip){ SceneManager.getInstance().getCurrentScene().updateLogic(); nextGameTick+=skipTicks; timeCorrection += (1000d/ticksPerSecond) % 1; nextGameTick+=timeCorrection; timeCorrection %=1; loops++; tics++; } extrapolation = (float)(System.currentTimeMillis() + skipTicks - nextGameTick) / (float)skipTicks; render(extrapolation); } Applying extrapolation render(float extrapolation){ //This example shows extrapolation for X axis only. Y position (spriteScreenY is assumed to be valid) extrapolatedPosX = spriteGridX+(SpriteXVelocity*dt)*extrapolation; spriteScreenPosX = extrapolationPosX * screenWidth; drawSprite(spriteScreenX, spriteScreenY); } Edit As I mentioned above, I have tried making a copy of the sprite's coordinates specifically to draw with.... this has it's own problems. Firstly, regardless of the copying, when the sprite is moving, it's super-smooth, when it stops, it's wobbling slightly left/right - as it's still extrapolating it's position based on the time. Is this normal behavior and can we 'turn it off' when the sprite stops? I've tried having flags for left / right and only extrapolating if either of these is enabled. I've also tried copying the last and current positions to see if there is any difference. However, as far as collision goes, these don't help. If the user is pressing say, the right button and the sprite is moving right, when it hits a wall, if the user continues to hold the right button down, the sprite will keep animating to the right, while being stopped by the wall (therefore not actually moving), however because the right flag is still set and also because the collision routine is constantly moving the sprite out of the wall, it still appear to the code (not the player) that the sprite is still moving, and therefore extrapolation continues. So what the player would see, is the sprite 'static' (yes, it's animating, but it's not actually moving across the screen), and every now and then it shakes violently as the extrapolation attempts to do it's thing....... Hope this help

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• Why is there no string interpolation in Scala?

  - by Alex R

  This is not just an idle quip... I wonder if anybody knows if there's an actual design reason why Scala does not support interpolation similar to Groovy and other "syntactically better Javas"? e.g. var str1 = "World"; var str2 = "Hello, ${str1}";

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• Interpolating between two networked states?

  - by Vaughan Hilts

  I have many entities on the client side that are simulated (their velocities are added to their positions on a per frame basis) and I let them dead reckon themselves. They send updates about where they were last seen and their velocity changes. This works great and other players see this work find. However, after a while these players begin to desync after some time. This is because of latency. I'd like to know how I can interpolate between states so they appear to be in the correct position. I know where the player was LAST seen and their current velocity but interpolating to the last seen state causes the player to actually move -backwards-. I could not use velocity at all for other clients and simply 'lerp' them towards the appropriate direction but I feel this would cause jaggy movement. What are the alternatives?

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• How do I interpolate air drag with a variable time step?

  - by Valentin Krummenacher

  So I have a little game which works with small steps, however those steps vary in time, so for example I sometimes have 10 Steps/second and then I have 20 Steps/second. This changes automatically depending on how many steps the user's computer can take. To avoid inaccurate positioning of the game's player object I use y=v0*dt+g*dt^2/2 to determine my objects y-position, where dt is the time since the last step, v0 is the velocity of my object in the beginning of my step and g is the gravity. To calculate the velocity in the end of a step I use v=v0+g*dt what also gives me correct results, independent of whether I use 2 steps with a dt of for example 20ms or one step with a dt of 40ms. Now I would like to introduce air drag. For simplicity's sake I use a=k*v^2 where a is the air drag's acceleration (I am aware that it would usually result in a force, but since I assume 1kg for my object's mass the force is the same as the resulting acceleration), k is a constant (in this case I'm using 0.001) and v is the speed. Now in an infinitely small time interval a is k multiplied by the velocity in this small time interval powered by 2. The problem is that v in the next time interval would depend on the drag of the last which again depends on the v of the last interval and so on... In other words: If I use a=k*v^2 I get different results for my position/velocity when I use 2 steps of 20ms than when I use one step of 40ms. I used to have this problem for my position too, but adding +g*dt^2/2 to the formula for my position fixed the problem since it takes into account that the position depends on the velocity which changes slightly in every infinitely small time interval. Does something like that exist for air drag too? And no, I dont mean anything like Adding air drag to a golf ball trajectory equation or similar, for that kind of method only gives correct results when all my steps are the same. (I hope you can understand my intermediate english, it's not my main language so I would like to say sorry for all the silly mistakes I might have made in my question)

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• Linear-time algorithms for sorting vertices in polygon contours

  - by Cheery

  I figured out an algorithm that lets me turn my holed polygons into trapezoids in linear time if I have vertex indices sorted from lowest coordinate to highest. I get simple polygons as contours. They have certain order that might be exploited most of the time. So giving these conditions, is there a near-linear-time algorithm on sorting?

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• How to make other semantics behave like SV_Position?

  - by object

  I'm having a lot of trouble with shadow mapping, and I believe I've found the problem. When passing vectors from the vertex shader to the pixel shader, does the hardware automatically change any of the values based on the semantic? I've compiled a barebones pair of shaders which should illustrate the problem. Vertex shader : struct Vertex { float3 position : POSITION; }; struct Pixel { float4 position : SV_Position; float4 light_position : POSITION; }; cbuffer Matrices { matrix projection; }; Pixel RenderVertexShader(Vertex input) { Pixel output; output.position = mul(float4(input.position, 1.0f), projection); output.light_position = output.position; // We simply pass the same vector in screenspace through different semantics. return output; } And a simple pixel shader to go along with it: struct Pixel { float4 position : SV_Position; float4 light_position : POSITION; }; float4 RenderPixelShader(Pixel input) : SV_Target { // At this point, (input.position.z / input.position.w) is a normal depth value. // However, (input.light_position.z / input.light_position.w) is 0.999f or similar. // If the primitive is touching the near plane, it very quickly goes to 0. return (0.0f).rrrr; } How is it possible to make the hardware treat light_position in the same way which position is being treated between the vertex and pixel shaders? EDIT: Aha! (input.position.z) without dividing by W is the same as (input.light_position.z / input.light_position.w). Not sure why this is.

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• Linear gradients library

  - by Lieven Cardoen

  Is there a place online where I can find like 16 linear gradients that match good with each other? I need them for a chart of mine and the ones generated (by Flex) aren't good enough. So, I'm kind off searching for a library of gradients (linear in my case).

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• linear interpolation on 8bit microcontroller

  - by JB

  I need to do a linear interpolation over time between two values on an 8 bit PIC microcontroller (Specifically 16F627A but that shouldn't matter) using PIC assembly language. Although I'm looking for an algorithm here as much as actual code. I need to take an 8 bit starting value, an 8 bit ending value and a position between the two (Currently represented as an 8 bit number 0-255 where 0 means the output should be the starting value and 255 means it should be the final value but that can change if there is a better way to represent this) and calculate the interpolated value. Now PIC doesn't have a divide instruction so I could code up a general purpose divide routine and effectivly calculate (B-A)/(x/255)+A at each step but I feel there is probably a much better way to do this on a microcontroller than the way I'd do it on a PC in c++ Has anyone got any suggestions for implementing this efficiently on this hardware?

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• OpenGL billboard interpolation issue

  - by PeanutPower

  I have a billboard quad with a texture mapped onto it. This is basically some text with transparency. The billboard floats forwards and backwards from the camera's perspective. As the billboard moves away (and appears smaller) there is an flickering effect around the edges of the text where there is a stroke border on the actual texture. I think this is because interpolation is needed as the image which is normally X pixels wide is now shown as only a % of X and some pixels need to be merged together. I guess it's doing nearest neighbour or something? Can anyone point me in the right direction for opengl settings to control this, I'm guessing there is some way of preventing this effect from happening by adjusting the method for how the texture is handled ?

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• WPF Animate a Matrix using interpolation

  - by Mark

  I'm having a issue with my application that is using touch gestures to scale, translate and rotate my scene. I was using a TransformGroup which contained TranslateTransform, ScaleTransform and a RotateTransform but I could not get the movement correct, it always jumps and skips, so I moved to a MaxtrixTransform which I was able to use much easier to get my scene to be zoomable, rotatable and panable nicely. However, what I later found out was that you cannot animate smoothly (using interpolation) the values of a Matrix, for what reason I have no idea, but its part of the MSDN doco and the properties of the Matrix are not dependency properties anyways... Has anyone had any luck animating a matrix to make it smooth? The only idea(s) I have had is to animate a few different, custom DP which all have callbacks that I update the matrix from OR To convert the matrix to a set of Transform objects that I then animate and then afterwords convert back. Is there a smarter way to do this?

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• WPF Animate a Maxtrix using interpolation

  - by Mark

  Im having a issue with my application that is using touch gestures to scale, translate and rotate my scene. I was using a TransformGroup which contained TranslateTransform, ScaleTransform and a RotateTransform but I could not get the movement correct, it always jumps and skips, so I moved to a MaxtrixTransform which I was able to use much easier to get my scene to be zoomable, rotatable and panable nicely. However, what I later found out was that you cannot animate smoothly (using interpolation) the values of a Matrix, for what reason I have no idea, but its part of the MSDN doco and the properties of the Matrix are not dependency properties anyways... Has anyone had any luck animating a maxtrix to make it smooth? The only idea(s) I have had is to animate a few different, custom DP which all have callbacks that I update the Matrix from OR To convert the Maxtix to a set of Transform object that I then animate and then afterwords convert back. Is there a smarter way to do this?

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• NET Math Libraries

  - by JoshReuben

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

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• How to choose an integer linear programming solver ?

  - by Cassie

  Hi all, I am newbie for integer linear programming. I plan to use a integer linear programming solver to solve my combinatorial optimization problem. I am more familiar with C++/object oriented programming on an IDE. Now I am using NetBeans with Cygwin to write my applications most of time. May I ask if there is an easy use ILP solver for me? Or it depends on the problem I want to solve ? I am trying to do some resources mapping optimization. Please let me know if any further information is required. Thank you very much, Cassie.

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• How to choose a integer linear programming solver ?

  - by Cassie

  Hi all, I am newbie for integer linear programming. I plan to use a integer linear programming solver to solve my combinational optimization problem. I am more familiar with C++/object oriented programming on an IDE. Now I am using NetBeans with Cygwin to write my applications most of time. May I ask if there is an easy use ILP solver for me? Or does it depend on the problem I want to solve ? I am trying to do some resources mapping optimization. please let me know if any further information is required. Thank you very much, Cassie.

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• How to find minimum of nonlinear, multivariate function using Newton's method (code not linear algeb

  - by Norman Ramsey

  I'm trying to do some parameter estimation and want to choose parameter estimates that minimize the square error in a predicted equation over about 30 variables. If the equation were linear, I would just compute the 30 partial derivatives, set them all to zero, and use a linear-equation solver. But unfortunately the equation is nonlinear and so are its derivatives. If the equation were over a single variable, I would just use Newton's method (also known as Newton-Raphson). The Web is rich in examples and code to implement Newton's method for functions of a single variable. Given that I have about 30 variables, how can I program a numeric solution to this problem using Newton's method? I have the equation in closed form and can compute the first and second derivatives, but I don't know quite how to proceed from there. I have found a large number of treatments on the web, but they quickly get into heavy matrix notation. I've found something moderately helpful on Wikipedia, but I'm having trouble translating it into code. Where I'm worried about breaking down is in the matrix algebra and matrix inversions. I can invert a matrix with a linear-equation solver but I'm worried about getting the right rows and columns, avoiding transposition errors, and so on. To be quite concrete: I want to work with tables mapping variables to their values. I can write a function of such a table that returns the square error given such a table as argument. I can also create functions that return a partial derivative with respect to any given variable. I have a reasonable starting estimate for the values in the table, so I'm not worried about convergence. I'm not sure how to write the loop that uses an estimate (table of value for each variable), the function, and a table of partial-derivative functions to produce a new estimate. That last is what I'd like help with. Any direct help or pointers to good sources will be warmly appreciated. Edit: Since I have the first and second derivatives in closed form, I would like to take advantage of them and avoid more slowly converging methods like simplex searches.

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