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• How can I save and read to XML the new C++ style matrix objects in OpenCV?

  - by neuviemeporte

  The old, C style cvMat matrices could be passed to the cvSave() function for easy writing to an XML file. The new C++ style cv::Mat and cv::Mat_ matrices are not accepted by this function. The OpenCV reference has a section on XML persistence, but the three classes (FileStorage, FileNode and FileNodeIterator) lack any description or example and I can't figure out how to use them from the interface. Thanks.

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• C++ Matrix class hierachy

  - by bpw1621

  Should a matrix software library have a root class (e.g., MatrixBase) from which more specialized (or more constrained) matrix classes (e.g., SparseMatrix, UpperTriangluarMatrix, etc.) derive? If so, should the derived classes be derived publicly/protectively/privately? If not, should they be composed with a implementation class encapsulating common functionality and be otherwise unrelated? Something else? I was having a conversation about this with a software developer colleague (I am not per se) who mentioned that it is a common programming design mistake to derive a more restricted class from a more general one (e.g., he used the example of how it was not a good idea to derive a Circle class from an Ellipse class as similar to the matrix design issue) even when it is true that a SparseMatrix "IS A" MatrixBase. The interface presented by both the base and derived classes should be the same for basic operations; for specialized operations, a derived class would have additional functionality that might not be possible to implement for an arbitrary MatrixBase object. For example, we can compute the cholesky decomposition only for a PositiveDefiniteMatrix class object; however, multiplication by a scalar should work the same way for both the base and derived classes. Also, even if the underlying data storage implementation differs the operator()(int,int) should work as expected for any type of matrix class. I have started looking at a few open-source matrix libraries and it appears like this is kind of a mixed bag (or maybe I'm looking at a mixed bag of libraries). I am planning on helping out with a refactoring of a math library where this has been a point of contention and I'd like to have opinions (that is unless there really is an objective right answer to this question) as to what design philosophy would be best and what are the pros and cons to any reasonable approach.

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• Implementation of a distance matrix of a binary tree that is given in the adjacency-list representation

  - by Denise Giubilei

  Given this problem I need an O(n²) implementation of this algorithm: "Let v be an arbitrary leaf in a binary tree T, and w be the only vertex connected to v. If we remove v, we are left with a smaller tree T'. The distance between v and any vertex u in T' is 1 plus the distance between w and u." This is a problem and solution of a Manber's exercise (Exercise 5.12 from U. Manber, Algorithms: A Creative Approach, Addison-Wesley (1989).). The thing is that I can't deal properly with the adjacency-list representation so that the implementation of this algorithm results in a real O(n²) complexity. Any ideas of how the implementation should be? Thanks.

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• Inverse dictionary lookup - Python

  - by RadiantHex

  Hi there, is there any straight forward way of finding a key by knowing the value within a dictionary? all I can think of is this: key = [i for key,value in dict.items() if value=='value' ][0] Any ideas?

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• building a pairwise matrix in scipy/numpy in Python from dictionaries

  - by user248237

  I have a dictionary whose keys are strings and values are numpy arrays, e.g.: data = {'a': array([1,2,3]), 'b': array([4,5,6]), 'c': array([7,8,9])} I want to compute a statistic between all pairs of values in 'data' and build an n by x matrix that stores the result. Assume that I know the order of the keys, i.e. I have a list of "labels": labels = ['a', 'b', 'c'] What's the most efficient way to compute this matrix? I can compute the statistic for all pairs like this: result = [] for elt1, elt2 in itertools.product(labels, labels): result.append(compute_statistic(data[elt1], data[elt2])) But I want result to be a n by n matrix, corresponding to "labels" by "labels". How can I record the results as this matrix? thanks.

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• i want to find determinant of 4x4 matrix in c#

  - by vj4u

  i want to find determinant of 4x4 matrix in c# please help urgent int ss = 4; int count = 0; int[,] matrix=new int[ss,ss]; ArrayList al = new ArrayList() {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 }; for (int i = 0; i < ss; i++) { for (int j = 0; j < ss; j++) { matrix[i, j] =Convert.ToInt32( al[count]); ++count; Response.Write(matrix[i, j] + " "); } Response.Write("<br/>"); }

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• Inverse function of FormatDateTime

  - by Salvador

  i am looking an funtion to reverse any string (YYYYMDD,YY/MM/DD,YYMMDD,...) created by the function FormatDateTime to datetime. example i have a string-date in format YYYYMMDDcreated by FormatDateTime mydatestr:=FormatDateTime('YYYYMMDD',Mydate); now how i can convert mydatestr to DateTime again?

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• Is the use of union in this matrix class completely safe?

  - by identitycrisisuk

  Unions aren't something I've used that often and after looking at a few other questions on them here it seems like there is almost always some kind of caveat where they might not work. Eg. structs possibly having unexpected padding or endian differences. Came across this in a math library I'm using though and I wondered if it is a totally safe usage. I assume that multidimensional arrays don't have any extra padding and since the type is the same for both definitions they are guaranteed to take up exactly the same amount of memory? template<typename T> class Matrix44T { ... union { T M[16]; T m[4][4]; } m; }; Are there any downsides to this setup? Would the order of definition make any difference to how this works?

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• R - indirectly calling a matrix using a string

  - by Boris Senderovich

  Example: There is a matrix of data called VE There is a vector of string where the first element is the string VE. I need to indirectly call the string and be able to access data. For example if I need the 6th column of matrix VE then I want to do: Vector[1][,6] Essentially I need R to start reading those string as if they are the matrix names that are already in this page. I need this syntax to be dynamic because I am putting it in a loop.

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• How do you concatenate the rows of a matrix into a vector in MATLAB?

  - by jimbo

  For an m-by-m (square) array, how do you concatenate all the rows into a column vector with size m^2 ?

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• Find largest rectangle containing only zeros in an N&times;N binary matrix

  - by Rajendra

  Given an NxN binary matrix (containing only 0's or 1's), how can we go about finding largest rectangle containing all 0's? Example: I 0 0 0 0 1 0 0 0 1 0 0 1 II->0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 <--IV 0 0 1 0 0 0 IV is a 6×6 binary matrix; the return value in this case will be Cell 1: (2, 1) and Cell 2: (4, 4). The resulting sub-matrix can be square or rectangular. The return value can also be the size of the largest sub-matrix of all 0's, in this example 3 × 4.

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• Problem with DirectX scene-graph

  - by Alex

  I'm trying to implement a basic scene graph in DirectX using C++. I am using a left child-right sibling binary tree to do this. I'm having trouble updating each node's world transformation relative to its parent (and its parent's parent etc.). I'm struggling to get it to work recursively, though I can get it to work like this: for(int i = 0; i < NUM_OBJECTS; i++) { // Initialize to identity matrix. D3DXMatrixIdentity(&mObject[i].toWorldXForm); int k = i; while( k != -1 ) { mObject[i].toWorldXForm *= mObject[k].toParentXForm; k = mObject[k].parent; } } toWorldXForm is the object's world transform and toParentXForm is the object's transform relative to the parent. I want to do this using a method within my object class (the code above is in my main class). This is what I've tried but it doesn't work (only works with nodes 1 generation away from the root) if (this->sibling != NULL) this->sibling->update(toParentXForm); D3DXMatrixIdentity(&toWorldXForm); this->toWorldXForm *= this->toParentXForm; this->toWorldXForm *= toParentXForm; toParentXForm *= this->toParentXForm; if (this->child != NULL) this->child->update(toParentXForm); Sorry if I've not been clear, please tell me if there's anything else you need to know. I've no doubt it's merely a silly mistake on my part, hopefully an outside view will be able to spot the problem.

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• Precision loss when transforming from cartesian to isometric

  - by Justin Skiles

  My goal is to display a tile map in isometric projection. This tile map has 25 tiles across and 25 tiles down. Each tile is 32x32. See below for how I'm accomplishing this. World Space World Space to Screen Space Rotation (45 degrees) Using a 2D rotation matrix, I use the following: double rotation = Math.PI / 4; double rotatedX = ((tileWorldX * Math.Cos(rotation)) - ((tileWorldY * Math.Sin(rotation))); double rotatedY = ((tileWorldX * Math.Sin(rotation)) + (tileWorldY * Math.Cos(rotation))); World Space to Screen Space Scale (Y-axis reduced by 50%) Here I simply scale down the Y value by a factor of 0.5. Problem And it works, kind of. There are some tiny 1px-2px gaps between some of the tiles when rendering. I think there's some precision loss somewhere, or I'm not understanding how to get these tiles to fit together perfectly. I'm not truncating or converting my values to non-decimal types until I absolutely have to (when I pass to the render method, which only takes integers). I'm not sure how to guarantee pixel perfect rendering precision when I'm rotating and scaling on a level of higher precision. Any advice? Do I need to supply for information?

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• How to do geometric projection shadows?

  - by John Murdoch

  I have decided that since my game world is mostly flat I don't need better shadows than geometric projections - at least for now. The only problem is I don't even know how to do those properly - that is to produce a 4x4 matrix which would render shadows for my objects (that is, I guess, project them on a horizontal XZ plane). I would like a light source at infinity (e.g., the sun at some point in the sky) and thus parallel projection. My current code does something that looks almost right for small flying objects, but actually is a very rude approximation, as it doesn't project the objects onto the ground, but simply moves them there (I think). Also it always wrongly assumes the sun is always on the zenith (projecting straight down). Gdx.gl20.glEnable(GL10.GL_BLEND); Gdx.gl20.glBlendFunc(GL10.GL_SRC_ALPHA, GL10.GL_ONE_MINUS_SRC_ALPHA); //shells shellTexture.bind(); shader.begin(); for (ShellState state : shellStates.values()) { transform.set(camera.combined); transform.mul(state.transform); shader.setUniformMatrix("u_worldView", transform); shader.setUniformi("u_texture", 0); shellMesh.render(shader, GL10.GL_TRIANGLES); } shader.end(); // shadows shader.begin(); for (ShellState state : shellStates.values()) { transform.set(camera.combined); m4.set(state.transform); state.transform.getTranslation(v3); m4.translate(0, -v3.y + 0.5f, 0); // TODO HACK: + 0.5f is a hack to ensure the shadow appears above the ground; this is overall a hack as we are just moving the shell to the surface instead of projecting it on the surface! transform.mul(m4); shader.setUniformMatrix("u_worldView", transform); shader.setUniformi("u_texture", 0); // TODO: make shadow black somehow shellMesh.render(shader, GL10.GL_TRIANGLES); } shader.end(); Gdx.gl.glDisable(GL10.GL_BLEND); So my questions are: a) What is the proper way to produce a Matrix4 to pass to openGL which would render the shadows for my objects? b) I am supposed to use another fragment shader for the shadows which would paint them in semi-transparent grey, correct? c) The limitation of this simplistic approach is that whenever there is some object on the ground (it is not flat) the shadows will not be drawn, correct? d) Do I need to add something very small to the y (up) coordinate to avoid z-fighting with ground textures? Or is the fact they will be semi-transparent enough to resolve that problem?

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• Glm Vector Transformations [duplicate]

  - by Reanimation

  This question already has an answer here: Car-like Physics - Basic Maths to Simulate Steering 2 answers I have a cube rendered on the screen which represents a car (or similar). Using Projection/Model matrices and Glm I am able to move it back and fourth along the axes and rotate it left or right. I'm having trouble with the vector mathematics to make the cube move forwards no matter which direction it's current orientation is. (ie. if I would like, if it's rotated right 30degrees, when it's move forwards, it travels along the 30degree angle on a new axes). I hope I've explained that correctly. This is what I've managed to do so far in terms of using glm to move the cube: glm::vec3 vel; //velocity vector void renderMovingCube(){ glUseProgram(movingCubeShader.handle()); GLuint matrixLoc4MovingCube = glGetUniformLocation(movingCubeShader.handle(), "ProjectionMatrix"); glUniformMatrix4fv(matrixLoc4MovingCube, 1, GL_FALSE, &ProjectionMatrix[0][0]); glm::mat4 viewMatrixMovingCube; viewMatrixMovingCube = glm::lookAt(camOrigin, camLookingAt, camNormalXYZ); vel.x = cos(rotX); vel.y=sin(rotX); vel*=moveCube; //move cube ModelViewMatrix = glm::translate(viewMatrixMovingCube,globalPos*vel); //bring ground and cube to bottom of screen ModelViewMatrix = glm::translate(ModelViewMatrix, glm::vec3(0,-48,0)); ModelViewMatrix = glm::rotate(ModelViewMatrix, rotX, glm::vec3(0,1,0)); //manually turn glUniformMatrix4fv(glGetUniformLocation(movingCubeShader.handle(), "ModelViewMatrix"), 1, GL_FALSE, &ModelViewMatrix[0][0]); //pass matrix to shader movingCube.render(); //draw glUseProgram(0); } keyboard input: void keyboard() { char BACKWARD = keys['S']; char FORWARD = keys['W']; char ROT_LEFT = keys['A']; char ROT_RIGHT = keys['D']; if (FORWARD) //W - move forwards { globalPos += vel; //globalPos.z -= moveCube; BACKWARD = false; } if (BACKWARD)//S - move backwards { globalPos.z += moveCube; FORWARD = false; } if (ROT_LEFT)//A - turn left { rotX +=0.01f; ROT_LEFT = false; } if (ROT_RIGHT)//D - turn right { rotX -=0.01f; ROT_RIGHT = false; } Where am I going wrong with my vectors? I would like change the direction of the cube (which it does) but then move forwards in that direction.

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• Excel 'Data Matrix'-Font

  - by ntor

  Is it possible in Excel to have a font that automatically generates a 'Data Matrix'-Code from a text string. (As it is possible for usual Barcodes) Would I perhaps have to use a Add-In, because the font isn't "linear" or "one-dimensional" as barcodes are? EDIT: I found a solution (using a pretty expensive software): I simply used "NiceLabel", which is capable of using XLS-Tables as databases. Then I generated the Codes (Could be Barcodes, QR-Codes, Data Matrix Codes) from the cells in Excel. This solution doesn't automatically generate a 2D-Code into an Excel-Cell but fits for my personal needs.

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• Fill rows down quickly (column or matrix of zeros)

  - by Mark Miller

  I have an extremely basic question, but I have never found the answer by searching the internet. I simply want to create a large column of zeros with Excel. Sometimes I want to create a huge matrix of zeros (maybe 600 rows by 500 columns) and then replace a few zeros with 1's to create a model design matrix. I have always started by creating a column of, for example, 10 zeros, copying and pasting those zeroes, then copying and pasting the resulting column of 20 zeros, etc., until I had the desired number of rows. Then I would copy and paste that column of zeros one at a time over and over until I had the desired number of columns. This procedure is tedious and time-consuming and I know there must be an easier way. Do you know of any other methods?

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• Direct3D11 and SharpDX - How to pass a model instance's world matrix as an input to a vertex shader

  - by Nathan Ridley

  Using Direct3D11, I'm trying to pass a matrix into my vertex shader from the instance buffer that is associated with a given model's vertices and I can't seem to construct my InputLayout without throwing an exception. The shader looks like this: cbuffer ConstantBuffer : register(b0) { matrix World; matrix View; matrix Projection; } struct VIn { float4 position: POSITION; matrix instance: INSTANCE; float4 color: COLOR; }; struct VOut { float4 position : SV_POSITION; float4 color : COLOR; }; VOut VShader(VIn input) { VOut output; output.position = mul(input.position, input.instance); output.position = mul(output.position, View); output.position = mul(output.position, Projection); output.color = input.color; return output; } The input layout looks like this: var elements = new[] { new InputElement("POSITION", 0, Format.R32G32B32_Float, 0, 0, InputClassification.PerVertexData, 0), new InputElement("INSTANCE", 0, Format.R32G32B32A32_Float, 0, 0, InputClassification.PerInstanceData, 1), new InputElement("COLOR", 0, Format.R32G32B32A32_Float, 12, 0) }; InputLayout = new InputLayout(device, signature, elements); The buffer initialization looks like this: public ModelDeviceData(Model model, Device device) { Model = model; var vertices = Helpers.CreateBuffer(device, BindFlags.VertexBuffer, model.Vertices); var instances = Helpers.CreateBuffer(device, BindFlags.VertexBuffer, Model.Instances.Select(m => m.WorldMatrix).ToArray()); VerticesBufferBinding = new VertexBufferBinding(vertices, Utilities.SizeOf<ColoredVertex>(), 0); InstancesBufferBinding = new VertexBufferBinding(instances, Utilities.SizeOf<Matrix>(), 0); IndicesBuffer = Helpers.CreateBuffer(device, BindFlags.IndexBuffer, model.Triangles); } The buffer creation helper method looks like this: public static Buffer CreateBuffer<T>(Device device, BindFlags bindFlags, params T[] items) where T : struct { var len = Utilities.SizeOf(items); var stream = new DataStream(len, true, true); foreach (var item in items) stream.Write(item); stream.Position = 0; var buffer = new Buffer(device, stream, len, ResourceUsage.Default, bindFlags, CpuAccessFlags.None, ResourceOptionFlags.None, 0); return buffer; } The line that instantiates the InputLayout object throws this exception: *HRESULT: [0x80070057], Module: [General], ApiCode: [E_INVALIDARG/Invalid Arguments], Message: The parameter is incorrect.* Note that the data for each model instance is simply an instance of SharpDX.Matrix. EDIT Based on Tordin's answer, it sems like I have to modify my code like so: var elements = new[] { new InputElement("POSITION", 0, Format.R32G32B32_Float, 0, 0, InputClassification.PerVertexData, 0), new InputElement("INSTANCE0", 0, Format.R32G32B32A32_Float, 0, 0, InputClassification.PerInstanceData, 1), new InputElement("INSTANCE1", 1, Format.R32G32B32A32_Float, 0, 0, InputClassification.PerInstanceData, 1), new InputElement("INSTANCE2", 2, Format.R32G32B32A32_Float, 0, 0, InputClassification.PerInstanceData, 1), new InputElement("INSTANCE3", 3, Format.R32G32B32A32_Float, 0, 0, InputClassification.PerInstanceData, 1), new InputElement("COLOR", 0, Format.R32G32B32A32_Float, 12, 0) }; and in the shader: struct VIn { float4 position: POSITION; float4 instance0: INSTANCE0; float4 instance1: INSTANCE1; float4 instance2: INSTANCE2; float4 instance3: INSTANCE3; float4 color: COLOR; }; VOut VShader(VIn input) { VOut output; matrix world = { input.instance0, input.instance1, input.instance2, input.instance3 }; output.position = mul(input.position, world); output.position = mul(output.position, View); output.position = mul(output.position, Projection); output.color = input.color; return output; } However I still get an exception.

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• C++ assignment operators dynamic arrays

  - by user2905445

  First off i know the multiplying part is wrong but i have some questions about the code. 1. When i am overloading my operator+ i print out the matrix using cout << *this then right after i return *this and when i do a+b on matix a and matix b it doesnt give me the same thing this is very confusing. 2. When i make matrix c down in my main i cant use my default constructor for some reason because when i go to set it = using my assignment operator overloaded function it gives me an error saying "expression must be a modifiable value. although using my constructor that sets the row and column numbers is the same as my default constructor using (0,0). 3. My assignment operator= function uses a copy constructor to make a new matrix using the values on the right hand side of the equal sign and when i print out c it doesn't give me anything Any help would be great this is my hw for a algorithm class which i still need to do the algorithm for the multiplying matrices but i need to solve these issues first and im having a lot of trouble please help. //Programmer: Eric Oudin //Date: 10/21/2013 //Description: Working with matricies #include <iostream> using namespace std; class matrixType { public: friend ostream& operator<<(ostream&, const matrixType&); const matrixType& operator*(const matrixType&); matrixType& operator+(const matrixType&); matrixType& operator-(const matrixType&); const matrixType& operator=(const matrixType&); void fillMatrix(); matrixType(); matrixType(int, int); matrixType(const matrixType&); ~matrixType(); private: int **matrix; int rowSize; int columnSize; }; ostream& operator<< (ostream& osObject, const matrixType& matrix) { osObject << endl; for (int i=0;i<matrix.rowSize;i++) { for (int j=0;j<matrix.columnSize;j++) { osObject << matrix.matrix[i][j] <<", "; } osObject << endl; } return osObject; } const matrixType& matrixType::operator=(const matrixType& matrixRight) { matrixType temp(matrixRight); cout << temp; return temp; } const matrixType& matrixType::operator*(const matrixType& matrixRight) { matrixType temp(rowSize*matrixRight.columnSize, columnSize*matrixRight.rowSize); if(rowSize == matrixRight.columnSize) { for (int i=0;i<rowSize;i++) { for (int j=0;j<columnSize;j++) { temp.matrix[i][j] = matrix[i][j] * matrixRight.matrix[i][j]; } } } else { cout << "Cannot multiply matricies that have different size rows from the others columns." << endl; } return temp; } matrixType& matrixType::operator+(const matrixType& matrixRight) { if(rowSize == matrixRight.rowSize && columnSize == matrixRight.columnSize) { for (int i=0;i<rowSize;i++) { for (int j=0;j<columnSize;j++) { matrix[i][j] += matrixRight.matrix[i][j]; } } } else { cout << "Cannot add matricies that are different sizes." << endl; } cout << *this; return *this; } matrixType& matrixType::operator-(const matrixType& matrixRight) { matrixType temp(rowSize, columnSize); if(rowSize == matrixRight.rowSize && columnSize == matrixRight.columnSize) { for (int i=0;i<rowSize;i++) { for (int j=0;j<columnSize;j++) { matrix[i][j] -= matrixRight.matrix[i][j]; } } } else { cout << "Cannot subtract matricies that are different sizes." << endl; } return *this; } void matrixType::fillMatrix() { for (int i=0;i<rowSize;i++) { for (int j=0;j<columnSize;j++) { cout << "Enter the matix number at (" << i << "," << j << "):"; cin >> matrix[i][j]; } } } matrixType::matrixType() { rowSize=0; columnSize=0; matrix = new int*[rowSize]; for (int i=0; i < rowSize; i++) { matrix[i] = new int[columnSize]; } } matrixType::matrixType(int setRows, int setColumns) { rowSize=setRows; columnSize=setColumns; matrix = new int*[rowSize]; for (int i=0; i < rowSize; i++) { matrix[i] = new int[columnSize]; } } matrixType::matrixType(const matrixType& otherMatrix) { rowSize=otherMatrix.rowSize; columnSize=otherMatrix.columnSize; matrix = new int*[rowSize]; for (int i = 0; i < rowSize; i++) { for (int j = 0; j < columnSize; j++) { matrix[i]=new int[columnSize]; matrix[i][j]=otherMatrix.matrix[i][j]; } } } matrixType::~matrixType() { delete [] matrix; } int main() { matrixType a(2,2); matrixType b(2,2); matrixType c(0,0); cout << "fill matrix a:"<< endl;; a.fillMatrix(); cout << "fill matrix b:"<< endl;; b.fillMatrix(); cout << a; cout << b; c = a+b; cout <<"matrix a + matrix b =" << c; system("PAUSE"); return 0; }

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• Calculating a Sample Covariance Matrix for Groups with plyr

  - by John A. Ramey

  I'm going to use the sample code from http://gettinggeneticsdone.blogspot.com/2009/11/split-apply-and-combine-in-r-using-plyr.html for this example. So, first, let's copy their example data: mydata=data.frame(X1=rnorm(30), X2=rnorm(30,5,2), SNP1=c(rep("AA",10), rep("Aa",10), rep("aa",10)), SNP2=c(rep("BB",10), rep("Bb",10), rep("bb",10))) I am going to ignore SNP2 in this example and just pretend the values in SNP1 denote group membership. So then, I may want some summary statistics about each group in SNP1: "AA", "Aa", "aa". Then if I want to calculate the means for each variable, it makes sense (modifying their code slightly) to use: > ddply(mydata, c("SNP1"), function(df) data.frame(meanX1=mean(df$X1), meanX2=mean(df$X2))) SNP1 meanX1 meanX2 1 aa 0.05178028 4.812302 2 Aa 0.30586206 4.820739 3 AA -0.26862500 4.856006 But what if I want the sample covariance matrix for each group? Ideally, I would like a 3D array, where the I have the covariance matrix for each group, and the third dimension denotes the corresponding group. I tried a modified version of the previous code and got the following results that have convinced me that I'm doing something wrong. > daply(mydata, c("SNP1"), function(df) cov(cbind(df$X1, df$X2))) , , = 1 SNP1 1 2 aa 1.4961210 -0.9496134 Aa 0.8833190 -0.1640711 AA 0.9942357 -0.9955837 , , = 2 SNP1 1 2 aa -0.9496134 2.881515 Aa -0.1640711 2.466105 AA -0.9955837 4.938320 I was thinking that the dim() of the 3rd dimension would be 3, but instead, it is 2. Really this is a sliced up version of the covariance matrix for each group. If we manually compute the sample covariance matrix for aa, we get: [,1] [,2] [1,] 1.4961210 -0.9496134 [2,] -0.9496134 2.8815146 Using plyr, the following gives me what I want in list() form: > dlply(mydata, c("SNP1"), function(df) cov(cbind(df$X1, df$X2))) $aa [,1] [,2] [1,] 1.4961210 -0.9496134 [2,] -0.9496134 2.8815146 $Aa [,1] [,2] [1,] 0.8833190 -0.1640711 [2,] -0.1640711 2.4661046 $AA [,1] [,2] [1,] 0.9942357 -0.9955837 [2,] -0.9955837 4.9383196 attr(,"split_type") [1] "data.frame" attr(,"split_labels") SNP1 1 aa 2 Aa 3 AA But like I said earlier, I would really like this in a 3D array. Any thoughts on where I went wrong with daply() or suggestions? Of course, I could typecast the list from dlply() to a 3D array, but I'd rather not do this because I will be repeating this process many times in a simulation. As a side note, I found one method (http://www.mail-archive.com/[email protected]/msg86328.html) that provides the sample covariance matrix for each group, but the outputted object is bloated. Thanks in advance.

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• Reporting Services - It's a Wrap!

  - by smisner

  If you have any experience at all with Reporting Services, you have probably developed a report using the matrix data region. It's handy when you want to generate columns dynamically based on data. If users view a matrix report online, they can scroll horizontally to view all columns and all is well. But if they want to print the report, the experience is completely different and you'll have to decide how you want to handle dynamic columns. By default, when a user prints a matrix report for which the number of columns exceeds the width of the page, Reporting Services determines how many columns can fit on the page and renders one or more separate pages for the additional columns. In this post, I'll explain two techniques for managing dynamic columns. First, I'll show how to use the RepeatRowHeaders property to make it easier to read a report when columns span multiple pages, and then I'll show you how to "wrap" columns so that you can avoid the horizontal page break. Included with this post are the sample RDLs for download. First, let's look at the default behavior of a matrix. A matrix that has too many columns for one printed page (or output to page-based renderer like PDF or Word) will be rendered such that the first page with the row group headers and the inital set of columns, as shown in Figure 1. The second page continues by rendering the next set of columns that can fit on the page, as shown in Figure 2.This pattern continues until all columns are rendered. The problem with the default behavior is that you've lost the context of employee and sales order - the row headers - on the second page. That makes it hard for users to read this report because the layout requires them to flip back and forth between the current page and the first page of the report. You can fix this behavior by finding the RepeatRowHeaders of the tablix report item and changing its value to True. The second (and subsequent pages) of the matrix now look like the image shown in Figure 3. The problem with this approach is that the number of printed pages to flip through is unpredictable when you have a large number of potential columns. What if you want to include all columns on the same page? You can take advantage of the repeating behavior of a tablix and get repeating columns by embedding one tablix inside of another. For this example, I'm using SQL Server 2008 R2 Reporting Services. You can get similar results with SQL Server 2008. (In fact, you could probably do something similar in SQL Server 2005, but I haven't tested it. The steps would be slightly different because you would be working with the old-style matrix as compared to the new-style tablix discussed in this post.) I created a dataset that queries AdventureWorksDW2008 tables: SELECT TOP (100) e.LastName + ', ' + e.FirstName AS EmployeeName, d.FullDateAlternateKey, f.SalesOrderNumber, p.EnglishProductName, sum(SalesAmount) as SalesAmount FROM FactResellerSales AS f INNER JOIN DimProduct AS p ON p.ProductKey = f.ProductKey INNER JOIN DimDate AS d ON d.DateKey = f.OrderDateKey INNER JOIN DimEmployee AS e ON e.EmployeeKey = f.EmployeeKey GROUP BY p.EnglishProductName, d.FullDateAlternateKey, e.LastName + ', ' + e.FirstName, f.SalesOrderNumber ORDER BY EmployeeName, f.SalesOrderNumber, p.EnglishProductName To start the report: Add a matrix to the report body and drag Employee Name to the row header, which also creates a group. Next drag SalesOrderNumber below Employee Name in the Row Groups panel, which creates a second group and a second column in the row header section of the matrix, as shown in Figure 4. Now for some trickiness. Add another column to the row headers. This new column will be associated with the existing EmployeeName group rather than causing BIDS to create a new group. To do this, right-click on the EmployeeName textbox in the bottom row, point to Insert Column, and then click Inside Group-Right. Then add the SalesOrderNumber field to this new column. By doing this, you're creating a report that repeats a set of columns for each EmployeeName/SalesOrderNumber combination that appears in the data. Next, modify the first row group's expression to group on both EmployeeName and SalesOrderNumber. In the Row Groups section, right-click EmployeeName, click Group Properties, click the Add button, and select [SalesOrderNumber]. Now you need to configure the columns to repeat. Rather than use the Columns group of the matrix like you might expect, you're going to use the textbox that belongs to the second group of the tablix as a location for embedding other report items. First, clear out the text that's currently in the third column - SalesOrderNumber - because it's already added as a separate textbox in this report design. Then drag and drop a matrix into that textbox, as shown in Figure 5. Again, you need to do some tricks here to get the appearance and behavior right. We don't really want repeating rows in the embedded matrix, so follow these steps: Click on the Rows label which then displays RowGroup in the Row Groups pane below the report body. Right-click on RowGroup,click Delete Group, and select the option to delete associated rows and columns. As a result, you get a modified matrix which has only a ColumnGroup in it, with a row above a double-dashed line for the column group and a row below the line for the aggregated data. Let's continue: Drag EnglishProductName to the data textbox (below the line). Add a second data row by right-clicking EnglishProductName, pointing to Insert Row, and clicking Below. Add the SalesAmount field to the new data textbox. Now eliminate the column group row without eliminating the group. To do this, right-click the row above the double-dashed line, click Delete Rows, and then select Delete Rows Only in the message box. Now you're ready for the fit and finish phase: Resize the column containing the embedded matrix so that it fits completely. Also, the final column in the matrix is for the column group. You can't delete this column, but you can make it as small as possible. Just click on the matrix to display the row and column handles, and then drag the right edge of the rightmost column to the left to make the column virtually disappear. Next, configure the groups so that the columns of the embedded matrix will wrap. In the Column Groups pane, right-click ColumnGroup1 and click on the expression button (labeled fx) to the right of Group On [EnglishProductName]. Replace the expression with the following: =RowNumber("SalesOrderNumber" ). We use SalesOrderNumber here because that is the name of the group that "contains" the embedded matrix. The next step is to configure the number of columns to display before wrapping. Click any cell in the matrix that is not inside the embedded matrix, and then double-click the second group in the Row Groups pane - SalesOrderNumber. Change the group expression to the following expression: =Ceiling(RowNumber("EmployeeName")/3) The last step is to apply formatting. In my example, I set the SalesAmount textbox's Format property to C2 and also right-aligned the text in both the EnglishProductName and the SalesAmount textboxes. And voila - Figure 6 shows a matrix report with wrapping columns. Share this post: email it! | bookmark it! | digg it! | reddit! | kick it! | live it!

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• NTRU Pseudo-code for computing Polynomial Inverses

  - by Neville

  Hello all. I was wondering if anyone could tell me how to implement line 45 of the following pseudo-code. Require: the polynomial to invert a(x), N, and q. 1: k = 0 2: b = 1 3: c = 0 4: f = a 5: g = 0 {Steps 5-7 set g(x) = x^N - 1.} 6: g[0] = -1 7: g[N] = 1 8: loop 9: while f[0] = 0 do 10: for i = 1 to N do 11: f[i - 1] = f[i] {f(x) = f(x)/x} 12: c[N + 1 - i] = c[N - i] {c(x) = c(x) * x} 13: end for 14: f[N] = 0 15: c[0] = 0 16: k = k + 1 17: end while 18: if deg(f) = 0 then 19: goto Step 32 20: end if 21: if deg(f) < deg(g) then 22: temp = f {Exchange f and g} 23: f = g 24: g = temp 25: temp = b {Exchange b and c} 26: b = c 27: c = temp 28: end if 29: f = f XOR g 30: b = b XOR c 31: end loop 32: j = 0 33: k = k mod N 34: for i = N - 1 downto 0 do 35: j = i - k 36: if j < 0 then 37: j = j + N 38: end if 39: Fq[j] = b[i] 40: end for 41: v = 2 42: while v < q do 43: v = v * 2 44: StarMultiply(a; Fq; temp;N; v) 45: temp = 2 - temp mod v 46: StarMultiply(Fq; temp; Fq;N; v) 47: end while 48: for i = N - 1 downto 0 do 49: if Fq[i] < 0 then 50: Fq[i] = Fq[i] + q 51: end if 52: end for 53: {Inverse Poly Fq returns the inverse polynomial, Fq, through the argument list.} The function StarMultiply returns a polynomial (array) stored in the variable temp. Basically temp is a polynomial (I'm representing it as an array) and v is an integer (say 4 or 8), so what exactly does temp = 2-temp mod v equate to in normal language? How should i implement that line in my code. Can someone give me an example. The above algorithm is for computing Inverse polynomials for NTRUEncrypt key generation. The pseudo-code can be found on page 28 of this document. Thanks in advance.

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• theoretical and practical matrix multiplication FLOP

  - by mjr

  I wrote traditional matrix multiplication in c++ and tried to measure and compare its theoretical and practical FLOP. As I know inner loop of MM has 2 operation therefore simple MM theoretical Flops is 2*n*n*n (2n^3) but in practice I get something like 4n^3 + number of operation which is 2 i.e. 6n^3 also if I just try to add up only one array a[i][j]++ practical flops then calculate like 3n^3 and not n^3 as you see again it is 2n^3 +1 operation and not 1 operation * n^3 . This is in case if I use 1D array in three nested loops as Matrix multiplication and compare flop, practical flop is the same (near) the theoretical flop and depend exactly as the number of operation in inner loop.I could not find the reason for this behaviour. what is the reason in both case? I know that theoretical flop is not the same as practical one because of some operations like load etc. system specification: Intel core2duo E4500 3700g memory L2 cache 2M x64 fedora 17 sample results: Matrix matrix multiplication 512*512 Real_time: 1.718368 Proc_time: 1.227672 Total flpops: 807,107,072 MFLOPS: 657.429016 Real_time: 3.608078 Proc_time: 3.042272 Total flpops: 807,024,448 MFLOPS: 265.270355 theoretical flop: 2*512*512*512=268,435,456 Practical flops= 6*512^3 =807,107,072 Using 1 dimensional array float d[size][size]:512 or any size for (int j = 0; j < size; ++j) { for (int k = 0; k < size; ++k) { d[k]=d[k]+e[k]+f[k]+g[k]+r; } } Real_time: 0.002288 Proc_time: 0.002260 Total flpops: 1,048,578 MFLOPS: 464.027161 theroretical flop: *4n^2=4*512^2=1,048,576* practical flop : 4n^2+overhead (other operation?)=1,048,578 3 loop version: Real_time: 1.282257 Proc_time: 1.155990 Total flpops: 536,872,000 MFLOPS: 464.426117 theoretical flop:4n^3 = 536,870,912 practical flop: *4n^3=4*512^3+overheads(other operation?)=536,872,000* thank you

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• creating matrix with probabilities

  - by John Chan

  Hi all, I want to generate a matrix of NxN to test some code that I have where each row contains floats as the elements and has to add up to 1 (i.e. a row with a set of probabilities). Where it gets tricky is that I want to make sure that randomly some of the elements should be 0 (in fact most of the elements should be 0 except for some random ones to be the probabilities). I need the probabilities to be 1/m where m is the number of elements that are not 0 within a single row. I tried to think of ways to output this, but essentially I would need this stored in a C++ array. So even if I output to a file I would still have the issue of not having it in array as I need it. At the end of it all I need that array because I want to generate a Market Matrix file. I found an implementation in C++ to take an array and convert it to the market matrix file, so this is what I am basing my findings on. My input for the rest of the code takes in this market matrix file so I need that to be the primary form of output. The language does not matter, I just want to generate the file at the end (I found a way mmwrite and mmread in python as well) Please help, I am stuck and not really sure how to implement this.

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• OPENGLES 2.0 equivalent of glorthof?

  - by Zippo

  Hi Guys, In my iphone app, i need to project 3d scene into the 2D coordinates of the screen for some calculations. My objects go through various rotations, translations and scaling. So i figured i need to multiply the vertices with ModelView matrix first, then i need to multiply it with the Orthogonal projection matrix. First of all am on the right track? I have the Model View Matrix, but need the projection matrix. Is there a glorthof equivalent in ES 2.0? PS: i am new to opengl. Thanks for your help. Zippo

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