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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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  • custom format specifications in python

    - by anupam
    hi, in python, how can a custom format-specification be added, to a class ? for example, if i write a matrix class, i would like to define a '%M' (or some such) which would then dump the entire contents of the matrix... thank you kind regards anupam

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  • How can I show a "selection highlighting"-rectangle around a column of a Silverlight Grid?

    - by carlmon
    I have a feature matrix implemented with Silverlight's Grid where users need to select a product. How can I indicate selection with a rectangle around the whole selected column? It is easy to put a CheckBox at the bottom of each product's column, but that is too dull. I would have preffered to use SL Toolkit's DataGrid (with built-in row selection), but it cannot be orientated vertically for a feature matrix... Thanks, Carl

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  • Preserve Font Size when scaling a Drawing

    - by serhio
    I do the following when drawing: Matrix m = new Matrix() m.Scale(_zoom, _zoom) e.Graphics.Transform = m e.Graphics.DrawLine(...) ' line representation e.Graphics.DrawString(...) ' line text Now, the text became also scaled. Is it possible to avoid it?

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  • Can a memory page be moved by modifying the page table?

    - by Adam
    Is it possible (on any reasonable OS, preferably Linux) to swap the contents of two memory pages by only modifying the page table and not actually moving any data? The motivation is a dense matrix transpose. If the data were blocked by page size it would be possible to transpose the data within a page (fits in cache) then swap pages to move the blocks into their final place. A large matrix would have many many pages moved, so hopefully flushing the TLB wouldn't cause trouble.

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  • Counting FLOPS/GFLOPS in program - CUDA

    - by msx
    Already finished my application which multiplies CRS matrix and vector (SpMV) and the only thing to do now is to count FLOPS my application did. In my opinion it's really hard to estimate number of floating point operation in case of sparse matrix - vector multiplication, because the number of multiplies in one row is really "jumpy" or fluent. I only tried to measure time using "cudaprof" ( available in ./CUDA/bin directory) - it works fine. Any sugestions and instruction pastes appreciated !

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  • Animating gradient displays line artifacts in ActionScript

    - by TheDarkIn1978
    i've programatically created a simple gradient (blue to red) sprite rect using my own basic class called GradientRect, but moving or animation the sprite exhibits line artifacts. when the sprite is rotating, it kind of resembles bad reception of an old television set. i'm almost certain the cause is because each line slice of the gradient is vector so there are gaps between the lines - this is visible when the sprite is zoomed in. var colorPickerRect:GradientRect = new GradientRect(200, 200, 0x0000FF, 0xFF0000); addChild(colorPickerRect); colorPickerRect.cacheAsBitmap = true; colorPickerRect.x = colorPickerRect.y = 100; colorPickerRect.addEventListener(Event.ENTER_FRAME, rotate); function rotate(evt:Event):void { evt.target.rotation += 1; } ________________________ //CLASS PACKAGE package { import flash.display.CapsStyle; import flash.display.GradientType; import flash.display.LineScaleMode; import flash.display.Sprite; import flash.geom.Matrix; public class GradientRect extends Sprite { public function GradientRect(gradientRectWidth:Number, gradientRectHeight:Number, ...leftToRightColors) { init(gradientRectWidth, gradientRectHeight, leftToRightColors); } private function init(gradientRectWidth:Number, gradientRectHeight:Number, leftToRightColors:Array):void { var leftToRightAlphas:Array = new Array(); var leftToRightRatios:Array = new Array(); var leftToRightPartition:Number = 255 / (leftToRightColors.length - 1); var pixelColor:Number; var i:int; //Push arrays for (i = 0; i < leftToRightColors.length; i++) { leftToRightAlphas.push(1); leftToRightRatios.push(i * leftToRightPartition); } //Graphics matrix and lineStyle var leftToRightColorsMatrix:Matrix = new Matrix(); leftToRightColorsMatrix.createGradientBox(gradientRectWidth, 1); graphics.lineStyle(1, 0, 1, false, LineScaleMode.NONE, CapsStyle.NONE); for (i = 0; i < gradientRectWidth; i++) { graphics.lineGradientStyle(GradientType.LINEAR, leftToRightColors, leftToRightAlphas, leftToRightRatios, leftToRightColorsMatrix); graphics.moveTo(i, 0); graphics.lineTo(i, gradientRectHeight); } } } } how can i solve this problem?

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  • What is the best way to run a loop of regressions in R?

    - by stevejb
    Assume that I have sources of data X and Y that are indexable, say matrices. And I want to run a set of independent regressions and store the result. My initial approach would be results = matrix(nrow=nrow(X), ncol=(2)) for(i in 1:ncol(X)) { matrix[i,] = coefficients(lm(Y[i,] ~ X[i,]) } But, loops are bad, so I could do it with lapply as out <- lapply(1:nrow(X), function(i) { coefficients(lm(Y[i,] ~ X[i,])) } ) Is there a better way to do this?

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  • MATLAB command for exporting geometry from pdetool

    - by lapwing
    I'm writing a MATLAB script which solves for the eigenmodes of a defined polygon. MATLAB's PDE toolbox lets me define the geometry using the command pdepoly() but I need to export the geometry description matrix manually to the workspace through the GUI before I can decompose, mesh, and solve the pde. Does anyone know either a command to export the geometry to the workspace or a better way to define this geometry description matrix in MATLAB? Many Thanks

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  • Package to compare LSA, TFIDF, Cosine metrics and Language Models

    - by gouwsmeister
    Hi, I'm looking for a package (any language, really) that I can use on a corpus of 50 documents to perform interdocument similarity testing in various metrics, like tfidf, okapi, language models, lsa, etc. I want as a result a document similarity matrix, i.e. doc1 is x% similar to doc2, etc... This is for research purposes, not for production. I specifically want the doc similarity matrix as I want to correlate this with human ratings. Thank you in advance!

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  • values from different fields in matalb

    - by ariel
    Hi does anybody familiar with a way that I could implement a matrix with values from a field (not the real or complex number, but lets say Z mod p). so I could perform all the operation of matlab on the matrix (with the values of the chosen field) Ariel

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  • Go - Using a container/heap to implement a priority queue

    - by Seth Hoenig
    In the big picture, I'm trying to implement Dijkstra's algorithm using a priority queue. According to members of golang-nuts, the idiomatic way to do this in Go is to use the heap interface with a custom underlying data structure. So I have created Node.go and PQueue.go like so: //Node.go package pqueue type Node struct { row int col int myVal int sumVal int } func (n *Node) Init(r, c, mv, sv int) { n.row = r n.col = c n.myVal = mv n.sumVal = sv } func (n *Node) Equals(o *Node) bool { return n.row == o.row && n.col == o.col } And PQueue.go: // PQueue.go package pqueue import "container/vector" import "container/heap" type PQueue struct { data vector.Vector size int } func (pq *PQueue) Init() { heap.Init(pq) } func (pq *PQueue) IsEmpty() bool { return pq.size == 0 } func (pq *PQueue) Push(i interface{}) { heap.Push(pq, i) pq.size++ } func (pq *PQueue) Pop() interface{} { pq.size-- return heap.Pop(pq) } func (pq *PQueue) Len() int { return pq.size } func (pq *PQueue) Less(i, j int) bool { I := pq.data.At(i).(Node) J := pq.data.At(j).(Node) return (I.sumVal + I.myVal) < (J.sumVal + J.myVal) } func (pq *PQueue) Swap(i, j int) { temp := pq.data.At(i).(Node) pq.data.Set(i, pq.data.At(j).(Node)) pq.data.Set(j, temp) } And main.go: (the action is in SolveMatrix) // Euler 81 package main import "fmt" import "io/ioutil" import "strings" import "strconv" import "./pqueue" const MATSIZE = 5 const MATNAME = "matrix_small.txt" func main() { var matrix [MATSIZE][MATSIZE]int contents, err := ioutil.ReadFile(MATNAME) if err != nil { panic("FILE IO ERROR!") } inFileStr := string(contents) byrows := strings.Split(inFileStr, "\n", -1) for row := 0; row < MATSIZE; row++ { byrows[row] = (byrows[row])[0 : len(byrows[row])-1] bycols := strings.Split(byrows[row], ",", -1) for col := 0; col < MATSIZE; col++ { matrix[row][col], _ = strconv.Atoi(bycols[col]) } } PrintMatrix(matrix) sum, len := SolveMatrix(matrix) fmt.Printf("len: %d, sum: %d\n", len, sum) } func PrintMatrix(mat [MATSIZE][MATSIZE]int) { for r := 0; r < MATSIZE; r++ { for c := 0; c < MATSIZE; c++ { fmt.Printf("%d ", mat[r][c]) } fmt.Print("\n") } } func SolveMatrix(mat [MATSIZE][MATSIZE]int) (int, int) { var PQ pqueue.PQueue var firstNode pqueue.Node var endNode pqueue.Node msm1 := MATSIZE - 1 firstNode.Init(0, 0, mat[0][0], 0) endNode.Init(msm1, msm1, mat[msm1][msm1], 0) if PQ.IsEmpty() { // make compiler stfu about unused variable fmt.Print("empty") } PQ.Push(firstNode) // problem return 0, 0 } The problem is, upon compiling i get the error message: [~/Code/Euler/81] $ make 6g -o pqueue.6 Node.go PQueue.go 6g main.go main.go:58: implicit assignment of unexported field 'row' of pqueue.Node in function argument make: *** [all] Error 1 And commenting out the line PQ.Push(firstNode) does satisfy the compiler. But I don't understand why I'm getting the error message in the first place. Push doesn't modify the argument in any way.

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  • Opengl Coordinate System

    - by praveen
    Say I am using an Identity Matrix for my modelViewTransformation Matrix on an Open GL ES2.0 program. The Co-ordinate system in this case is the canonical opengl co-ordinate system which extends from (-1,-1,-1) to (1,,1,1). My question is, is this coordinate system right-handed or left-handed? A broader question: Is there a document with OpenGL which can list all the mathematical conventions followed by the API?

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  • Managed DirectX as a starting point

    - by numerical25
    I know the difference between manage and unmanaged DirectX. My question is if I decided to do managed directX as a starting point, would it help me to better understand unmanaged DirectX. Honestly, the only thing I see different about the 2 is how you initiate and access resources. Matrix Math is Matrix no matter what so If I learn it in managed, then I should be fine in unmanaged

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  • Silverlight - DataTable

    - by Villager
    Hello, I have a need to basically create a matrix of values in my Silverlight 3 application. Is there anything equivalent to a DataTable that I could store a matrix of values within? Thank you,

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  • MATLAB image corner coordinates & referncing to cell arrays

    - by James
    Hi, I am having some problems comparing the elements in different cell arrays. The context of this problem is that I am using the bwboundaries function in MATLAB to trace the outline of an image. The image is of a structural cross section and I am trying to find if there is continuity throughout the section (i.e. there is only one outline produced by the bwboundaries command). Having done this and found where the is more than one section traced (i.e. it is not continuous), I have used the cornermetric command to find the corners of each section. The code I have is: %% Define the structural section as a binary matrix (Image is an I-section with the web broken) bw(20:40,50:150) = 1; bw(160:180,50:150) = 1; bw(20:60,95:105) = 1; bw(140:180,95:105) = 1; Trace = bw; [B] = bwboundaries(Trace,'noholes'); %Traces the outer boundary of each section L = length(B); % Finds number of boundaries if L > 1 disp('Multiple boundaries') % States whether more than one boundary found end %% Obtain perimeter coordinates for k=1:length(B) %For all the boundaries perim = B{k}; %Obtains perimeter coordinates (as a 2D matrix) from the cell array end %% Find the corner positions C = cornermetric(bw); Areacorners = find(C == max(max(C))) % Finds the corner coordinates of each boundary [rowindexcorners,colindexcorners] = ind2sub(size(Newgeometry),Areacorners) % Convert corner coordinate indexes into subcripts, to give x & y coordinates (i.e. the same format as B gives) %% Put these corner coordinates into a cell array Cornerscellarray = cell(length(rowindexcorners),1); % Initialises cell array of zeros for i =1:numel(rowindexcorners) Cornerscellarray(i) = {[rowindexcorners(i) colindexcorners(i)]}; %Assigns the corner indicies into the cell array %This is done so the cell arrays can be compared end for k=1:length(B) %For all the boundaries found perim = B{k}; %Obtains coordinates for each perimeter Z = perim; % Initialise the matrix containing the perimeter corners Sectioncellmatrix = cell(length(rowindexcorners),1); for i =1:length(perim) Sectioncellmatrix(i) = {[perim(i,1) perim(i,2)]}; end for i = 1:length(perim) if Sectioncellmatrix(i) ~= Cornerscellarray Sectioncellmatrix(i) = []; %Gets rid of the elements that are not corners, but keeps them associated with the relevent section end end end This creates an error in the last for loop. Is there a way I can check whether each cell of the array (containing an x and y coordinate) is equal to any pair of coordinates in cornercellarray? I know it is possible with matrices to compare whether a certain element matches any of the elements in another matrix. I want to be able to do the same here, but for the pair of coordinates within the cell array. The reason I don't just use the cornercellarray cell array itself, is because this lists all the corner coordinates and does not associate them with a specific traced boundary.

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  • Manage DirectX as a starting point

    - by numerical25
    I know the difference between manage and unmanaged DirectX. My question is if I decided to do managed directX as a starting point, would it help me to better understand unmanaged DirectX. Honestly, the only thing I see different about the 2 is how you initiate and access resources. Matrix Math is Matrix no matter what so If I learn it in managed, then I should be fine in unmanaged

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  • What's the best way to draw a fullscreen quad in OpenGL 3.2?

    - by Phineas
    I'm doing ray casting in the fragment shader. I can think of a couple ways to draw a fullscreen quad for this purpose. Either draw a quad in clip space with the projection matrix set to the identity matrix, or use the geometry shader to turn a point into a triangle strip. The former uses immediate mode, deprecated in OpenGL 3.2. The latter I use out of novelty, but it still uses immediate mode to draw a point.

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  • How to distort the desktop screen

    - by HaifengWang
    Hi friends, I want to change the shape of the desktop screen, so what are displayed on the desktop will be distorted at the same time. And the user can still operate the PC with the mouse on the distorted desktop(Run the applications, Open the "My Computer" and so on). I think I must get the projection matrix of the screen coordinate at first. Then transform the matrix, and map the desktop buffer image to the distorted mesh. Are there any interfaces which can modify the shape of the desktop screen in OpenGL or DirectX? Would you please give me some tip on it. Thank you very much in advance. Please refer to the picture from http://oi53.tinypic.com/bhewdx.jpg BR, Haifeng Addition1: I'm sorry! Maybe I didn't express clearly what I want to implement. What I want to implement is to modify the shape of the screen. So we can distort the shapes of all the applications which are run on Windows at the same time. For example that the window of "My Computer" will be distorted with the distortion of the desktop screen. And we can still operate the PC with mouse from the distorted desktop(Click the shortcut to run a program). Addition2: The projection matrix is just my assume. There isn't any desktop projection matrix by which the desktop surface is projected to the screen. What I want to implement is to change the shape of the desktop, as the same with mapping the desktop to an 3D mesh. But the user can still operate the OS on the distorted desktop(Click the shortcut to run a program, open the ie to surf the internet). Addition3: The shapes of all the programs run on the OS are changed with the distortion of the screen. It's realtime. The user can still operate the OS on the distorted screen as usually. Maybe we can intercept or override the GPU itself to implement the effect. I'm investigating GDI, I think I can find some clue for that. The first step is to find how to show the desktop on the screen.

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