svd | 易学教程

Singular values calculation only with CUDA

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问题 I'm trying to use the new cusolverDnSgesvd routine of CUDA 7.0 for the calculation of the singular values. The full code is reported below: #include "cuda_runtime.h" #include "device_launch_parameters.h" #include <stdio.h> #include<iostream> #include<stdlib.h> #include<stdio.h> #include <cusolverDn.h> #include <cuda_runtime_api.h> /***********************/ /* CUDA ERROR CHECKING */ /***********************/ void gpuAssert(cudaError_t code, char *file, int line, bool abort=true) { if (code !=

Matlab SVD output in opencv

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问题 in Matlab SVD function outputs three Matrices: [U,S,V] = svd(X) and we can use the S Matrix to find to smallest possible number of component to reduce the dimension of X to retain enough variance. My question is how can I find the S Matrix (not the U Matrix) using Opencv , Is it possible to find S Matrix using build in OpenCV SVD? I mean OpenCV SVD function outputs three matrices like the Matlab one, But I don't know if they are the same or not. this is the SVD in OpenCV: SVD::compute

How to reconstruct original matrix from svd components with Spark

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问题 I want to reconstruct (the approximation of) the original matrix decomposed in SVD. Is there a way to do this without having to convert the V factor local Matrix into a DenseMatrix ? Here is the decomposition based on the documentation (note that the comments are from the doc example) import org.apache.spark.mllib.linalg.Matrix import org.apache.spark.mllib.linalg.SingularValueDecomposition import org.apache.spark.mllib.linalg.Vector import org.apache.spark.mllib.linalg.distributed.RowMatrix

SciPy SVD vs. Numpy SVD

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问题 Both SciPy and Numpy have built in functions for singular value decomposition (SVD). The commands are basically scipy.linalg.svd and numpy.linalg.svd . What is the difference between these two? Is any of them better than the other one? 回答1: Apart from the error checking, the actual work seems to be done within lapack both with numpy and scipy . Without having done any benchmarking, I guess the performance should be identical. 回答2: From the FAQ page, it says scipy.linalg submodule provides a

Correct way to extract Translation from Essential Matrix through SVD

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问题 I calibrated my camera and found the intrinsic parameters(K). Also I have calculated the Fundamental Matrix (F). Now E= K_T* F * K . So far so good. Now we pass the Essential Matrix(E) to the SVD to use the decomposition values (U,W,V) to extract the Rotation and Translation: essentialMatrix = K.Transpose().Mul(fund).Mul(K); CvInvoke.cvSVD(essentialMatrix, wMatrix, uMatrix, vMatrix, Emgu.CV.CvEnum.SVD_TYPE.CV_SVD_DEFAULT); ** Question) At this point, two methods have been proposed, and it has

reconstruct time series from SSA

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问题 let us consider following code clear all; B=xlsread('data_generations1','A1','g8:g301'); n=length(B); L =input('Give the size of the interval: ' );% Number of columns in the Data matrix m=n-L+1;%number of rows in the Data matrix X = zeros(m,L); for i=1:m X(i,:)=B(i:i+L-1); end; S=X*X'; [U,autoval]=eig(S); [d,i]=sort(-diag(autoval)); d=-d; U=U(:,i);sev=sum(d); plot((d./sev)*100),hold on,plot((d./sev)*100,'rx'); title('Singular Spectrum');xlabel('Eigenvalue Number');ylabel('Eigenvalue (% Norm

How to fill NaN values in numeric array to apply SVD?

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问题 I am combined two data-frames that have some common columns, however there are some different columns. I would like to apply Singular Value Decomposition (SVD) on the combined data-frame. However, filling NaN values will affect the results, even filling the data with zeros will be wrong in my case since there are some columns have zero values. Here's an example. Is there any ways to address this issue ?. >>> df1 = pd.DataFrame(np.random.rand(6, 4), columns=['A', 'B', 'C', 'D']) >>> df1 A B C

Using alternative LAPACK driver in numpy's svd method?

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问题 I'm using numpy.svd to compute singular value decompositions of badly conditioned matrices. For some special cases the svd won't converge and raise a Linalg.Error. I've done some research and found that numpy uses the DGESDD routine from LAPACK. The standard implementation has a hardcoded iteration limit of 35 or something iterations. If I try to decompose the same matrix in Matlab, everything works fine, and I think there's two reasons for that: 1. Matlab uses DGESVD instead of DGESDD which

强大的矩阵奇异值分解(SVD)及其应用

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一、奇异值与特征值基础知识：特征值分解和奇异值分解在机器学习领域都是属于满地可见的方法。两者有着很紧密的关系，我在接下来会谈到，特征值分解和奇异值分解的目的都是一样，就是提取出一个矩阵最重要的特征。先谈谈特征值分解吧： 1）特征值：如果说一个向量v是方阵A的特征向量，将一定可以表示成下面的形式：这时候λ就被称为特征向量v对应的特征值，一个矩阵的一组特征向量是一组正交向量。特征值分解是将一个矩阵分解成下面的形式：其中Q是这个矩阵A的特征向量组成的矩阵，Σ是一个对角阵，每一个对角线上的元素就是一个特征值。我这里引用了一些参考文献中的内容来说明一下。首先，要明确的是，一个矩阵其实就是一个线性变换，因为一个矩阵乘以一个向量后得到的向量，其实就相当于将这个向量进行了线性变换。比如说下面的一个矩阵：它其实对应的线性变换是下面的形式：因为这个矩阵M乘以一个向量(x,y)的结果是：上面的矩阵是对称的，所以这个变换是一个对x，y轴的方向一个拉伸变换（每一个对角线上的元素将会对一个维度进行拉伸变换，当值>1时，是拉长，当值<1时时缩短），当矩阵不是对称的时候，假如说矩阵是下面的样子：它所描述的变换是下面的样子：这其实是在平面上对一个轴进行的拉伸变换（如蓝色的箭头所示），在图中，蓝色的箭头是一个最主要的变化方向（变化方向可能有不止一个），如果我们想要描述好一个变换

矩阵特征值分解与奇异值分解含义解析及应用

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特征值与特征向量的几何意义矩阵的乘法是什么，别只告诉我只是“前一个矩阵的行乘以后一个矩阵的列”，还会一点的可能还会说“前一个矩阵的列数等于后一个矩阵的行数才能相乘”，然而，这里却会和你说——那都是表象。矩阵乘法真正的含义是变换，我们学《线性代数》一开始就学行变换列变换，那才是线代的核心——别会了点猫腻就忘了本——对，矩阵乘法就是线性变换，若以其中一个向量A为中心，则B的作用主要是使A发生如下变化： 1、伸缩 clf; A = [0, 1, 1, 0, 0;... 1, 1, 0, 0, 1]; % 原空间 B = [3 0; 0 2]; % 线性变换矩阵 plot(A(1,:),A(2,:), '-*');hold on grid on;axis([0 3 0 3]); gtext('变换前'); Y = B * A; plot(Y(1,:),Y(2,:), '-r*'); grid on;axis([0 3 0 3]); gtext('变换后'); 从上图可知，y方向进行了2倍的拉伸，x方向进行了3倍的拉伸，这就是B=[3 0; 0 2]的功劳,3和2就是伸缩比例。请注意，这时B除了对角线元素为各个维度的倍数外，非正对角线元素都为0，因为下面将要看到，对角线元素非0则将会发生切变及旋转的效果。 2、切变 clf; A = [0, 1, 1, 0, 0;... 1, 1, 0