# 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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### 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 ...
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### 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 (<...
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### 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 ...
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### Compute eigenvectors of a matrix with known eigenvalue spectrum

If I have already accurately known the eigenvalue spectrum (i.e. all eigenvalues) of a matrix, is there any efficient numerical algorithm to compute all the eigenvectors corresponding to these ...
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### Simple way to derive transpose of a vectorized operation

In a program I'm writing, I have a sub-routine that does some vectorized linear operations (specifically differentiation). Say for convenience I have defined the following inline function, which ...
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### Difference between eigendecomposition and singular value decomposition for Hermitian matrices

Let consider the following Hermitian matrix ...
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### Solve eigenvalue problem using finite differences without vectorization

I am interested in solving the problem $-A u = \lambda u$ on a finite differences grid on a square. In my case, the operator $A$ is of the type $-\Delta + \mu I$, where $\mu$ is there to impose some ...
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### How big a matrix can we row reduce in reasonable time?

I have very large matrices that I would like to row reduce (I need to keep track of the steps and find a basis of the kernel/image, not just find the rank). The good news is that I work mod 2 and the ...
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### What is a good way to take fractional powers of a matrix in MATLAB?

I am working on a problem that involves taking fractional powers of particular matrices. For the matrix A with 2 on the main diagonal and -1 on the sub and super diagonal (the finite difference ...
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### Why is my MATLAB code for back-substitution slower than the backslash operator?

I wrote the code below to invert an upper triangular matrix, avoiding any possible multiplication/subtraction by zero. It just uses $\frac{1}{6}n^3+\ldots$ flops instead of $n^3+\ldots$ flops. ...
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### Optimizing rank computation for very large sparse matrices

I have a sparse matrix such as ...
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### smallest eigenvalues for linear elasticity

I want to compute a few tens of the smallest eigenvalues of a linear system which is a discretization of a linear elasticity. In the presence of additional constraints like Dirichlet boundary ...
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### Are there any popular (paralleled) implementations of Lanczos methods for SVD/eigendecomposion?

I want to use it in Matlab or Java. Will these two languages be much slower for computing the algorithm compared to C, C++, in case efficiency is an important factor? I'm aware of that there's a ...
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### Can anyone give me some suggestions about optimize my Matlab codes?

recently, I try to write a Matlab codes to implement a sparse approximation inverse factorization method proposed by M. Benzi in his paper http://www.mathcs.emory.edu/~benzi/Web_papers/ainv.pdf this ...
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### Are there any algorithms “incrementally remove part of data (esp., old data)” from the existing SVD model of a data?

Sometimes it is meaningful to remove the influence of some old data from a SVD-based model, so as to reflect the most updated trends and provide more accurate results. I've seen there're incremental ...
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### Minimize quadratic form with equality constraints

I want to minimize function: $f(x) = x^T \cdot A \cdot x + b \cdot x$ given constraints: $B \cdot x = 0$. Here: $x$ is a vector ($x \in \mathbb{R}^n$), $A$ is a matrix of size $n \times n$, $b$ ...
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### Large overdetermined system of linear equations

I'm looking for a method to solve a large overdetermined system of linear equations in a least squares sense. The matrix is dense. I'd like to use a method that works even with limited memory (we can'...
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### Are there improved method of computing the following expression?

given a symmetric matrix $Y \in \mathbb{R}^{n \times n}$, and an arbitrary matrix $X \in \mathbb{R}^{n \times n}$, and a vector $v \in \mathbb{R}^{n \times 1}$, is it possible to compute the following ...
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### Does it matter if I use principal component analysis on the transpose instead of the original matrix?

My data set is a 60x10 matrix. I performed principal component analysis of this matrix with matlab using the princomp(AdjustedData) after I adjusting my original data set by subtracting the mean of ...
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### Azimuthal average in Fortran? Find indexes in Fortran?

I am working on an eigenvalue problem in fortran. I have used Lapack to solve the problem and get the eigenvalues and eigenvectors. This is done for $201\times101$ wavenumbers, only half the wavespace ...
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### Translate a 3D point along a heading

I need to translate a point (P1) in 3D a certain amount, call it stepSize, along a vector described by a heading composed of ...
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### Writing a 3D array from Petsc

I am trying to do something fairly simple somehow I have made it hard. Is there an example of how to send a 3D array to a binary file?
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