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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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4
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1answer
400 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
346 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
246 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 ...
4
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1answer
97 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 ...
2
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2answers
307 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 ...
2
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2answers
182 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.
1
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1answer
149 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: $$...
3
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2answers
989 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 ...
1
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1answer
186 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 ...
6
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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 ...
1
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1answer
465 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
117 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
104 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 $N \times N$ ...
6
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0answers
403 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
428 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 ...
1
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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 ...
0
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1answer
302 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 <...
2
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1answer
211 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
854 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
votes
1answer
86 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 ...
1
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1answer
155 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
71 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. ...
2
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1answer
363 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 ...
0
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1answer
92 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 $A^{-1}$ ...
3
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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 ...
1
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1answer
212 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
426 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 ...
4
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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 <...
1
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1answer
262 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
votes
3answers
518 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, ...
1
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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 ...
3
votes
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. ...
3
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1answer
294 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 ...
1
vote
1answer
706 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 ...
1
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0answers
262 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 ...
2
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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 ...
3
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0answers
123 views

What is the computational cost of using complex numbers in contrast to real numbers in matrix operations, e.g. $LU$ or $LDL^T$ factorizations? [duplicate]

I am curious about how much one loses in terms of computational cost, when complex numbers are used instead of real numbers? I guess the number of floating point operations and memory doubles, but I ...
1
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2answers
1k views

How can I prove that two eigenvectors are orthogonal?

I obtained 6 eigenpairs of a matrix using eigs of Matlab. How can I demonstrate that these eigenvectors are orthogonal to each other? I am almost sure that I ...
4
votes
2answers
2k views

Optimization with matrix determinant as constraint

I'm solving a constrained optimization for matrix $\mathbf{A}$ with dimension 6x6, where one of the constraints is $\mathrm{det}(\mathbf{A})>0$. I use the NLopt package to solve my problem and ...
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1answer
188 views

Solving large system of equations, is linear programming best option? [closed]

I have a problem where I am trying to solve many systems of equations, that have very few variables per equation, but a lot of equations. For example potentially 10 variables max in a single equation,...
1
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2answers
3k views

How to use the basic Sparse matrix operations (multiplication, .etc) in PyCUDA

I try to use sparse matrix operations in GPU in Python and now try to use PyCUDA with theano. But I can't find how to do sparse matrix and vector multiplication. I only got an example showing how to ...
4
votes
1answer
482 views

Numerically stable approach for calculating x in Ax=b

I have an equation $Ax=b$ for which I need to solve for numerous $x$ matrices given $b$. Both $x$ and $b$ are nx1 matrices. Unfortunately, $A$ is a 32x32 matrix and inversion gives highly unstable ...
2
votes
1answer
134 views

Is my matrix symmetric?

I obtained a mass matrix through Finite Elements discretization. Now, I want to check if it is symmetric. To do that I subtract to my matrix $M$ its transposed $M^T$. The result is another matrix of ...
9
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1answer
27k views

What is the fastest algorithm for computing the inverse matrix and its determinant for positive definite symmetric matrices?

Given a positive definite symmetric matrix, what is the fastest algorithm for computing the inverse matrix and its determinant? For problems I am interested in, the matrix dimension is 30 or less. ...
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2answers
799 views

Parallelization of element-wise matrix multiplication

I use Armadillo as an interface to OpenBLAS. In my current program, I have a loop, in which I do multiplications of the form ...
6
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0answers
111 views

How does an unpivoted QR fail to reveal rank?

An unpivoted QR factorization produces a triangular factor $R$. A rank-revealing QR factorization is typically done with column pivoting. My question is, how does an unpivoted QR factorization fail to ...
8
votes
6answers
10k views

Super C++ optimization of matrix multiplication with Armadillo

I'm using Armadillo to do very intensive matrix multiplications with side lengths $2^n$, where $n$ can be up to 20 or even more. I'm using Armadillo with OpenBLAS for matrix multiplication, which ...
2
votes
1answer
779 views

Solve Ax=B where B is a matrix in parallell

I try to solve the problem $Ax=B$ where $A$ is a large sparse $n\times n$ matrix, and $B$ is a dense $n\times m$ matrix (here $n=754850$ and $m=182$). The backslash operator yields correct solution (<...
0
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1answer
265 views

Standard Algorithms for Permuting CCS or CRS Sparse Matrices

I need to permute the degrees of freedom of a system and apply this permutation to a few sparse matrices in CCS (or CRS) format. I could construct a permutation matrix and perform sparse matrix-matrix ...