Questions tagged [matrix]

Matrix is a rectangular array of elements (e.q. numbers, symbols, or expressions), arranged in columns and rows.

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1answer
293 views

Calculating adjacency matrix of platonic solids

I need to devise a algorithm (in Python) that calculates adjacency matrices for the platonic solids. Inputted into the algorythm needs to be the number of polygons meeting at each vertex and the ...
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1answer
158 views

Finding all binary vectors with given A-length

I am given a $n \times n$ matrix $A$ with real entries and define the inner product $$\langle x,y\rangle = x^T A y.$$ I am also given an integer $k$ and need to find all binary vectors $x$ such that $...
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123 views

Inverse of “diagonally not dominant matrix”

I want to frame a higher order Central difference scheme of about $20^{th}$ order for first derivative. I'm using $20^{th}$ order because I need one scheme with good modified wave number. To find the ...
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1answer
1k views

Armadillo library appears slow

I have been experimenting in building a C++ project for a FDTDS system for Electro-Magnetics. I have implemented a class [see below] which I called mesh using the Armadillo library. The 3D matrices {...
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1answer
39 views

How to use compiled python packages for matrix initialization

Assume I have an expression for an matrix initialization, for example the following: A[i,i-2*j+k] = B[i-k] * C[i] * D[i+j+k] In order to execute such a process, I could loop over all i, j and k. ...
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7k views

In FEM, why is the stiffness matrix positive definite?

In FEM classes, it's usually taken for granted that the stiffness matrix is positive definite, but I just can't understand why. Could anyone give some explanation? For instance, we can consider the ...
2
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1answer
149 views

MATLAB : Does the qr algorithm and the DGEMM used in MATLAB take into account if the input matrix is tridigonal and optimize accordingly?

Let's say we want to solve for the eigen-values of a symmetric matrix of size $n$ x $n$. In the Phase 1 of the computation, the matrix is reduced to a tridigonal form using Householder/Arnoldi's ...
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1answer
308 views

How to compute the Jacobi matrix (tridiagonal matrix) of a polynomial with a recurrence relationship?

I am looking at Trefethen and Bau Exercise 37.1: I have two normalizations of the Legendre polynomials with corresponding recurrence relations: $$P_n(1)=1$$ which follows $$P_n(x) = \frac{2n-1}{n} x ...
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265 views

Fast computation of component-wise $\exp(-XY^T)G$ for random $G$

I have the following question: Suppose I have two matrices $X, Y$ both of size $m\times p$ and a random i.i.d Gaussian matrix $G$ of size $m \times k$, $m\gg p>k$. Is there a fast way to compute $...
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2answers
135 views

Matlab Vectorization of columns in a 2D matrix and single element multiplication

MATLAB. I am trying to vectorize a loop in which each column vector of a 2D matrix (n-by-n) is found by multiplying each single element in a diagonal matrix with a column vector in another n-by-n 2D ...
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2answers
254 views

Optimized parallel routine for $X' W X$ with $W$ diagonal

$X$ is a dense matrix of real doubles, typically of size 20 million rows and 500 columns, and $W$ is a diagonal matrix of real, non-negative doubles stored as a vector. I'm working in C and have ...
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1answer
121 views

Get a matrix with absolute values in PETSc [closed]

Is there any function to create or change a matrix, to have $A_{ij} = \text{abs}(A_{ij})$ in PETSc? If possible it should work with MPIAIJ matrices, not only local.
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410 views

Fast algorithm for computing matrix square root using randomized linear algebra?

Is there a fast algorithm for computing the matrix square root of a real symmetric matrix using random matrices or randomized algorithms?
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1answer
424 views

Obtaining column vectors of pseudo-inverse of a matrix

I need to compute the pseudo-inverse of a very large rectangular dense matrix without any special structure or properties. I run out of memory/computing power and have no access to a large parallel ...
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1answer
361 views

Kernel of a Sparse Matrix

Given a sparse rectangular matrix $A$ (let's say, with dimension $n,m$ and number of non-zero elements $O(n)\sim O(m)$) with entries in $\mathbb Z/2\mathbb Z$ I'm looking for a basis of the kernel as ...
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3answers
252 views

How to find closed form $C$ such that $CC^T = AA^T + BB^T$

How to find $C$ such that $CC^T = AA^T + BB^T$, $A$ and $B$ are known. $A = \left(\begin{matrix}X\\Y\end{matrix}\right)$, $B = \left(\begin{matrix}0\\cY\end{matrix}\right)$, $c$ is a constant. To ...
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1answer
102 views

Does $\log(\det(A))$ equals sum of log of diagonal elements of D in LDLT decomposition?

For a large matrix $A$, I need to evaluate the $\log(\det(A))$. I already have it's LDLT decomposition. Is it possible to evaluate the $\log\det$ with the elements of the diagonal $D$ of the LDLT ...
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2answers
323 views

QR decomposition

I have a matrix which is "almost" like an upper triangular just that the last row has non zero elements. And I want to perform the QR decomposition on that matrix. Does anyone know the "name" of such ...
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2answers
210 views

Generation of random Matrix with Real eigen values

does anyone know any matlab algorithm that can help me generate a random matrix with REAL EIGEN values? Thanks.
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1answer
150 views

Max size of set linear equations to solve? (X=AX+B)

This question has also been asked at Stack Overflow. This is a very general question regarding the maximum size of a set of linear equations to be solved by today's fastest hardware, in the form: $$...
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2answers
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Efficently invert tiny matrix in Fortran

I have a piece of code in Fortran90 in which I have to solve both a non-linear (with the Newton-Raphson method, for which I have to invert the Jacobian matrix) and a linear system of equations. When I ...
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1answer
199 views

Compare reconstruction of matrices using SVD

I'm interested in how much 'signal' is retained from including k singular values in a Singular Value Decomposition, but I'm having trouble conceptualizing (or ...
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2answers
3k views

Calculating the log-determinant of a large sparse matrix

I need to calculate $\log(\det (\mathbf M_i))$ where the $\mathbf M_i$'s are large sparse matrices, which are real, symmetric and positive semi-definite. I hope to have between $10$ and $100$ of ...
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1answer
488 views

On the fly/matrix free SVD of large sparse matrix

I am trying to apply SVD to large sparse matrices. I already compared the performances of Propack and irlba to those of the matlab svd and ...
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0answers
120 views

Hessian eigenvalues in 4D-VAR data assimilation

I am using variational data assimilation (4D-VAR) to estimate emissions of anthropogenic greenhouse gases using a rather complex atmospheric transport model. Hence, the optimal solution to my problem ...
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1answer
109 views

Sparse Matrix Reordering

Matrix reorderings are important for many direct solvers. Sometimes the objective is to reduce the bandwith or the generated fill in by LU Decomposition. I am interested in a reordering which reduces ...
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1answer
1k views

Efficiently extracting a submatrix in Matlab

Suppose I have this matrix in Matlab R2013a M = kron(A,B); where A and B are $N \times N$ ...
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427 views

What is the source of the error in the Sherman-Morrison formula application?

The Sherman-Morrison formula $$ (A+uv^T)^{-1} = A^{-1} - \frac{A^{-1}uv^TA^{-1}}{1+v^TA^{-1}u} $$ results in small errors in relation to the standard matrix inverse operation after each application, ...
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1answer
453 views

How to convert MPIAIJ to SEQAIJ matrix in petsc/petsc4py?

I am curious, if there is a function to convert MPIAIJ (distributed matrices in AIJ format) to a SEQAIJ matrix that lie on a single processor. It is possible to do such an operation for PETSc vectors ...
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0answers
74 views

fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like $$ [A][X]=C\times\big(\exp([B][X])-1\big), $$ where $C$ is a ...
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1answer
337 views

Efficient method to multiply floating point matrix with binary matrix and get double precision results

I have a matrix A which is of size (n2, n1) and I am multiplying it by a matrix, B, of size <...
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1answer
218 views

How to calculate $det(X^TX)$ efficiently, update one column of X each time

$X_{1} = (A, b)$, where $X_{1}$ is a $n\times p$ matrix, $A$ is a $n\times (p-1)$ and $b$ is $n\times1$. update $b$ with $c$,Is there any update method to compute more efficiently?
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1answer
886 views

How to represent a binary number in a matrix in Matlab?

This is a fairly simple question but my Matlab knowledge is still very limited. I want to take a given binary number (or rather, a bistring) of length $mn$ and generate an $m \times n$ matrix whose ...
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1answer
94 views

Is there an efficient $O(n^2)$ way to get the eigen decomposition given a LDL factorization?

Let's say I have a LDL factorization of a matrix A. Is there an efficient $O(n^2)$ way to get the eigen decomposition of A given it's LDL factorization? Is there a more efficient way, in case L and ...
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1answer
156 views

solve linear system of equation of a large sparse symetric positive definite matrix

I want to invert large matrices ($10^4 \times 10^4$ to $10^6 \times 10^6$) but sparse (less than $100$ non-zero entries per line) on clusters with $16$ to $48$ processors per node. I'm looking for an ...
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1answer
72 views

Is there an efficient $O(n^2)$ way to estimate in MATLAB a matrix condition number given its LDL decomposition?

Since evaluating a matrix condition number usually takes $O(n^3)$, I wonder whether there is an efficient $O(n^2)$ way to estimate in MATLAB a matrix condition number given its LDL decomposition. ...
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1answer
379 views

Recommendation for C/C++ library which offers Schur complement functions?

I need to find C/C++ libraries which offer function for computing Schur complement. I know about MUMPS and Pastix, but I need more of them to compare them in my research. Do you have any experience ...
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1answer
95 views

Evaluating a quadratic form with an inverse of a sparse PD matrix, comparison between using the inverse vs using a Cholseky decomposition

I have the following quadratic form I need to evaluate: $x^T A^{-1} y$, where $A$ is a sparse positive definite matrix, $x, y$ are sparse vectors. Now assume that I am given for free both $A^{-1}$ ...
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2answers
1k views

SVD of large block-hankel matrix

I am trying to do SVD of a large block-hankel matrix for model order reduction (Low rank approximation). However, I quickly run into memory issues in forming the large Block-Hankel matrix and CPU ...
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1answer
213 views

$AX=B$: How to solve for $X$ if elements of matrix A are matrices

Objective: I am trying to solve for $C$ in 2D space (x,y) and time from following PDE. $$ \text{PDE: }\frac{\partial C}{\partial t} + \nabla\left(v.C - D\nabla{C} \right)= \alpha.C $$ Method: I ...
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1answer
441 views

ADR equation implicit solution: Penta-diagonal matrix for a 2D $N\times N$ system

Objective: I am trying to simulate the following advection-diffusion-reaction equation in 2D space (x,y) and time. $$\begin{align} \text{ADR Equation: }\frac{\partial C}{\partial t} + \nabla\left(v.C ...
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1answer
1k views

What is wrong with this matrix multiplication?

I am attempting to write a matrix multiplication routine because I need to do some analysis in CUDA and I want to validate it with CPU code. I am trying to use <...
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1answer
283 views

Fast algorithms for computing only the generalized singular values (but not the vectors)

I am interested in computing only the generalized singular values, and was wondering if this was faster (and by how much?) than computing the full GSVD. In particular, I was wondering what the ...
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3answers
528 views

Exact analytical matrix inversion of sparse 100x100 matrices in C++

I need to invert a matrix. Of course, I'm not the first person in this situation, and I know that there's a wealth of powerful libraries out there, of which I only know a couple. That being said, ...
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1answer
113 views

Is this the correct procedure for calculating matrix spectrum?

I am not sure if my question is on topic but I have a piece of Fortran code that is used to perform successive over relaxation. Prior to performing successive over relaxation the author is calculating ...
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2answers
2k views

BLAS, LAPACK or ATLAS for Matrix Multiplication in C

I am trying to find the most optimized way to perform Matrix Multiplication of very large sizes in C language and under Windows 7 or Ubuntu 14.04. And searching led me to BLAS, LAPACK and ATLAS. ...
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1answer
300 views

Sparse matrix vector product using PETSC

I am trying to do a simple parallel sparse matrix vector multiplications using PETSC. My sparse matrix is a simple tridiagonal laplacian matrix, which is distributed over multiple processors using ...
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1answer
757 views

Convert Image of Map to 2D Grid in Python

I have this map showing the geography of Europe (below), and I wish to convert it to a matrix in python that would be a 2D approximation of this image where 0's would represent the ocean and 1's would ...
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0answers
267 views

How can I efficiently solve $Ax$=$b$ given $A$ is symmetric and contains very small (even negative) eigenvalues using EIGEN

Currently I am using the EIGEN C++ library to try to solve $x$ from the equation $Ax$ = $b$. One problem I encountered is that the matrix $A$ is a correlation matrix with size > 5000 and can ...
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1answer
102 views

How do I make sparse solvers to accept custom matvec function insted of matrix?

I have tried it with Lis, Intel mkl and PETSc. Everywhere you need to pass an actual matrix ...

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