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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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499 views

Solve $AX=B$ where $A$ is a skyline matrix

Solve a matrix equation of the type $AX=B$, where $A$ is an $n \times n$ symmetric matrix stored in the form of symmetric skyline matrix. With the solution given by Bill and some more research on ...
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0answers
195 views

Extracting sinograms from tomography projections

my name is Lorenzo and I am a postdoc researcher in Italy. My job is related to tomography imaging using synchrotron radiation. This is a new field for me and I start to face with Matlab to write some ...
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3answers
1k views

How to compute the rank of a large sparse matrix in MATLAB

I am interested in computing the ranks of fairly large, the largest being of magnitude $10^6$ x $10^6$, sparse matrices whose entires are all 0, 1, or -1. I have been trying to use Matlab to ...
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1answer
260 views

What category is this problem?

My first question, please excuse me if its too basic. I have a matrix of evenly spaced geographical points; say 10 x 10, which I will call seed points. Each seed ...
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1answer
103 views

Finding the matrix inverse given a solver for the matrix equation $Ax=b$

So I'm given a solver that can solve for $x$ in the matrix equation $\underset{=}{A} \underline{x} = \underline{b}$ where $b$ can be anything we specify. (NB: A is an NxN matrix). I now want to find ...
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1answer
230 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 ...
6
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1answer
121 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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2answers
108 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
38 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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2answers
6k 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 ...
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1answer
137 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
217 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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1answer
260 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
131 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
183 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 ...
3
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1answer
109 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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1answer
317 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
347 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 ...
2
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1answer
286 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
237 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
81 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
253 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
150 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
148 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
916 views

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
168 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
424 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 ...
2
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0answers
113 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 ...
3
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1answer
100 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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0answers
334 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, ...
2
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1answer
389 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
72 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
250 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
201 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
770 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 ...
4
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1answer
78 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
152 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 ...
3
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1answer
68 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
327 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
84 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
210 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
391 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
236 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 ...
3
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3answers
489 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
112 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 ...