Questions tagged [matrix]
For questions about using and representing matrices on a computer in order to solve computational problems. Should generally also include a tag about the specific property/problem you are solving (e.g. [tag:linear-algebra], [tag:eigenvalues], [tag:inverse].
585
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2
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1
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Parallelize pseudo inverse of a matrix using Lapacke
I am currently using the protocol described in
https://stackoverflow.com/questions/55599950/computation-of-pseidoinverse-with-svd-in-c-using-blas-and-lapacke to compute the pseudo inverse of a matrix.
...
4
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5
answers
612
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Matrix derivative
I am looking to compute the derivative of the following expression:
$$\frac{\partial}{\partial X}\mathrm{tr}\left[A\exp(X)\right]$$
where $A$ is both a symmetrical and positive-definite matrix and $X$ ...
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3
votes
1
answer
80
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Scipy solve_ivp sensitivity to random phase shifts
I am trying to solve a coupled system of ODE's using the solve_ivp function from scipy. The general form of the equation is given via
$$\dot{y}(t) = M(t)y(t).$$
The time dependence of matrix is ...
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0
votes
1
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97
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How to efficiently transpose distributed matrix in Scalapack?
I have a distributed matrix in block cyclic layout. Is there an efficient way to out/in place transpose a distributed matrix with scalapack?
Context: I am trying to diagonalize the transpose of a ...
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3
votes
1
answer
119
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Rewriting quadratically-constrained optimization problem as a semidefinite program
Suppose $A,H$ are positive definite matrices and $\alpha,t$ are scalars. Is there a way to massage the following problem into a form suitable for a specialized solver?
$$\begin{array}{ll} \underset{\...
- 1,799
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0
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80
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Does cblas_dgemm mutate my input matrices?
I have written a matrix class Matrix<T> for which I have implemented a wrapper function for cblas_dgemm.
...
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0
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3
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142
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How do we compute a matrix-vector product without using the standard matrix multiplication?
I am a bit confused right now. I am taking a class on numerical linear algebra and as I have understood sometimes one doesn't compute the Matrix-Vector product $Av$ normally but uses other techniques ...
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1
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1
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77
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QR decomposition with only diagonal elements changing
I have to compute the QR decomposition of a matrix A repeatedly, each time with ONLY diagonal elements changing. Is there an efficient way to accomplish this ...
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3
votes
1
answer
148
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BiCGSTAB convergence
So I need a fast converging solver for SysLinEq as a subroutine in fortran, decided to test BiCGStab in Matlab.
Thank God I decided to test it out on first before implementing in Fortran as a ...
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2
votes
1
answer
195
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Matrix regularisation for ill-conditioned problems
I have read that matrix regularisation can improve the stability of LU or Cholesky decomposition of ill conditioned problems. The idea is to add a value to the diagonals of a matrix:
$B=A+cI$
In the ...
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2
votes
0
answers
43
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Is there a permutation used in sparse QR factorizations that better locates small elements on the diagonal of R?
Is there a permutation used in sparse QR factorizations that better locates small elements on the diagonal of R to the end of the diagonal? As an example, consider the following snippet of MATLAB ...
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5
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2
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308
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Recurrence relation for matrices
I have matrices ($S_0$ thought $S_N$) and I have a recurrence relation that link successive matrices together.
$$S_i + S_i(aS_{i-1}^{-1})S_i=C_i+aS_{i+1}$$
We can assume for this problem that $S_0=S_N=...
- 436
5
votes
0
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43
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Lowest eigenvalues of a matrix with divergent entries
In high energy physics we oftentimes encounter the following problem. For a given parametrized matrix $\{H_{ij}(\Lambda)\}$, we know that in the limit $\Lambda\to\infty$ some of its entries become ...
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votes
1
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Using submatrices of matrix decomposition for solving a large number least-squares problems
I want to decrease the computational time for solving a large number (>1000) of least-squares problems. Given a matrix, the system matrix for each least-squares problem is a submatrix of the given ...
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1
vote
1
answer
112
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constructing a symmetric matrix for finite difference
I come across the following operator in a paper
$\mathcal{I}\psi = \psi_{xxxx} + (r~\psi_x)_x$,
where $\psi=\psi(x)$ and $r=r(x)$. Periodic boundary condition is employed. It claims that the operator $...
- 217
0
votes
1
answer
925
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Dynamic Sized Identity Matrix in Eigen
I am aware of creating an identity matrix in Eigen if the number of rows and columns are known. How do we create them dynamically when the size is not known? An example would be useful. Thanks.
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2
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Calculate average distance between pairs of points without computing full distance matrix
Suppose I have a set of $N$ points of shape $N \times D$, where $D$ is the dimensionality. I want to compute the average Euclidean distance between all points, as well as additional moments such as ...
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1
vote
1
answer
91
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Fast algorithm to compute chi-square
I would like to evaluate the chi-square of the form $\chi^2=v^{T}C^{-1}v$ where $v$ is a column vector and $C$ is a covariance matrix. Both $v$ and $C$ are known and $C$ is a $740\times740$ matrix. ...
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1
answer
73
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Converting a 4 rank matrix to 2 rank matrix after using tensorproduct
Let's say I have a 2x2 matrix (with symbols) called 'A'. Now, if do
B = sympy.tensorproduct(A,A)
print(sympy.shape(B))
I get,
...
5
votes
1
answer
280
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Converting distance matrix back into original data
Suppose that we have $N$ points, and a distance matrix $D \in \mathbb{R}^{N \times N}$ describing the Euclidean distance among those points. For now, assume that we do not necessarily know how many ...
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4
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2
answers
192
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nnz-preserving sparse matrix multiplication
Let A and B be sparse matrices in $ \mathbb{R}^{m\times m}$ with (roughly) the same density $p$. I want to efficiently compute a matrix $C$ that in some sense is "closest" to $AB$ while ...
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vote
0
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478
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Symmetric Matrix in Eigen C++
I am aware of a symmetric matrix type in uBLAS as ublas::symmetric_matrix matrix. Is there an equivalent for this in Eigen library that can be used to construct one or do we need to explicitly check ...
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0
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147
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Trouble inverting complex matrix with numpy and scipy
I have some matrix-valued, complex data $Z(f)$ with $f\in\{f_0,f_1,\dots\}$ and $Z(f_i)$ being a 3x3 matrix. I require the inverse $Z^{-1}(f)$ in my workflow. After encountering some problems with my ...
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0
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Is this a legit way to sample a random matrix spectrum?
In order to undergird a theoretical model concerning many body physics, I want to have exponentially large eigenvalue spectra from the random matrix GOE ensemble. its properties are mainly
(i) a ...
0
votes
2
answers
130
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Implementation of $[X, \cdot]$ as an $n^2 \times n^2$ matrix, where $X$ is an $n \times n$ matrix
Let $M_n(\mathbb{R})$ denote the set of $n\times n$ matrices with real entries. I have an $n\times n$ matrix $X\in M_n(\mathbb{R})$, and I would like to implement the linear operator $[X, \cdot] : M_n(...
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votes
1
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217
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Algorithm for solving systems which are nearly symmetric/adjoint?
I am familiar with Cholesky decomposition and LU factorization for solving systems of linear equations.
I have a problem where I have large sparse matrices (say, 1000x1000 or larger) where only one or ...
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18
votes
3
answers
3k
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Why do we usually not want the eigenvalues of non-symmetric matrices?
I came across this line in a class note I am reading where it discusses finding eigenvalues of matrices.
In reality we don't go all the way with Arnoldi. We stop at a decent value of 𝑘. Then the 𝑘 ...
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1
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1
answer
436
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Efficiency of scipy.sparse.linalg.expm_multiply with sparse vs unsparse vectors
From the package scipy.sparse.linalg in Python, calling expm_multiply(X, v) allows you to compute the vector ...
- 185
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1
answer
255
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2-norm and infinty norm of a system in controls
How to compute 2-norm or infinity norm of following system?
i am confused whether to calculate using simple matrix theory "where it don't regard for s domain" or H2 and H-infinty norm. ...
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1
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1
answer
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What is difference between L2 norm and H2 Norm?
When someone refers 2-norm of system,L2 and H2 are used interchangeably by author and is rather confusing. Even the matlab has different functions for H-infinity norm and L-infinity norm.
as shown in ...
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0
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Matlab - Equality between 2 Fisher matrices constructed in a different way
I want to know if, on a Fisher matrix, the projection operation (with a Jacobian matrix) commutes with a matricial inversion operation.
The 2 ways to build these 2 matrices are:
1) First method:
1.1) ...
0
votes
0
answers
83
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Can a symmetric matrix be found using matrix-vector operation while maintaining matrix-vector operatin?
Consider $A\in\mathbb{R}^{n\times n}$ its not a special matrix and in the worst case all of its entries are non-zero. I am looking for a way to compute $AA^{T}$ using matrix-vector operation. The ...
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0
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Do the projection (with Jacobian) and marginalisation (inversion of matrix and remove a row/column and reinversion) commute?
I try to check the equality or the inequality between 2 Fisher matrices.
The goal is too see if the projection (with Jacobian) and marginalisation (inversion of matrix and remove a row/column and ...
1
vote
2
answers
434
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Dyadic operations, fourth order tensors and Tensor algebra
I am trying to understand the dyadic operation for a while since I am interested in Elasticity problems. I believe an intuitive understanding (rather than assuming) will give me good problem solving ...
2
votes
1
answer
121
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Vectorization Matlab/Octave of Markov Matrix Powers
I have just created a code snippet in Octave/Matlab that aims to create a plot which shows the accuracy of an initial probability vector $\vec{\pi}$ derived from the transition probability matrix $\...
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1
vote
1
answer
107
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RCM better than Nested dissection? (For FEM discretizations in 2D and 3D)
I realize this might be a too general question but here goes nothing:
I am trying different re-ordering strategies and checking the fill-in of $A=LU$.
I have 2D ($p=1$, $h=1/40$ on $\Omega = [-1,1]^2$)...
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2
votes
0
answers
149
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Jacobian matrix cutoff in ODE solver
I am studying an implementation of a 3rd semi-implicit Runge Kutta method (siRK3) from the book by Villadsen & Michelsen (1978), Solution of differential equation models by polynomial ...
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4
votes
1
answer
130
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How are Matrices Stored in MATLAB?
I have this simple question but I am trying to figure out why:
Are matrices stored column-wise in MATLAB? If so then why?
I theorize that they are stored column-wise because the memory does not have ...
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3
votes
1
answer
137
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Forming a particular (averaged) block matrix with numpy
Say I have a set of $n \times n$ matrices $A_1, ..., A_m$ as numpy arrays. I'd like to create the block matrix defined below.
I'm looking for a clean, elegant, and easy-to-interpret way of doing this ...
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1
vote
1
answer
409
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MATLAB : find an algorithm to inverse quickly a large matrix of symbolic variables
I have to solve the equality between 2 matrixes 12x12 containing a lot of symbolic variables and with which I perform inversion of matrix. There is only one unknown called "...
0
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1
answer
260
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Pseudospectrum of non square Matrix in Python
I have a rectangular matrix $A \in \mathbb{R}^{m \times n}$
...
user38211
8
votes
3
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924
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Accurate Way to Calculate Matrix Powers and Matrix Exponential for Sparse Positive Semidefinite Matrices
I do need to numerically calculate the following forms for any $x\in\mathbb{R}^n$, possibly in python:
$x^T M^k x$, where $M\in\mathbb{R^{n\times n}}$ is a PSD sparse matrix, $n$ can be quite large ...
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votes
0
answers
64
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How to solve this boundary value problem which has more unknown than equation on MATLAB
I need your helps about solving the problem below with MATLAB. I am trying to solve 2D Stress Wave Propagation problem by using FDTD(Finite difference time domain) method on the cylindrical coord. I ...
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2
votes
1
answer
697
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How to Invert a Poorly Conditioned Matrix
In my research, I need to invert a Fisher matrix in order to get a covariance matrix for me to do parameter estimation. Unfortunately, the values of Fisher matrix vary by many orders of magnitude, and ...
3
votes
1
answer
308
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Quick way to find a common basis of eigenvectors between 2 matrices : valid or not?
Following the advise of @Federico Polonion a previous post, one suggested, to find a basis of common eigen vectors between 2 matrices, to simply do :
Generate 2 ...
2
votes
2
answers
248
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Matlab - Compute approximative common eigenvectors basis between two matrices as a function of tolerance
I am looking for finding or rather building common eigenvectors matrix X between 2 matrices A and B such as :
...
11
votes
1
answer
5k
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How to compute Singular value decomposition of a large matrix with Python
Language: Python3
Problem: I have a matrix Q of shape [51200 rows x 51200 cols] stored in a binary file, each of the element in this matrix has a data type of complex64. To load the data into memory I ...
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6
votes
1
answer
434
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Efficiently computing $e^{tX}$ for many different values of $t$
Given an anti-Hermitian and sparse matrix $X$, I am using Python (NumPy and SciPy) to compute the matrix exponential $f(t) := e^{tX}$ for many values of $t$. The method I am currently using is to ...
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vote
0
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What's the best way to implement a least-squares estimation of a motor system in MATLAB?
Basically, I'm trying to use Least-Squares to estimate the parameters of a DC motor.
My system can be modeled by the following matrix equation:
$$\begin{bmatrix}V_{input}(t)\\0\end{bmatrix}=\begin{...
- 109
1
vote
0
answers
45
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updating the matrix Adjugate/Cofactor
I would like to calculate the Adjugate matrix of a given matrix $A$, and its updates in the diagonal:
$B=A-\lambda I$, where $I$ is the identity matrix, $\lambda$ is a scalar. To this end, I am using ...
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