Questions tagged [sparse]

Problems in which an operator or function can be represented with asymptotically less data than the naive representation. Not limited to sparse matrices.

212 questions
39 views

Plotting ratings matrix

Hello fellows and folks. I have been looking to do this for 1 month and still cannot find the way to do it. Here’s what’s going on: I have a csv file called ratings.csv with the following ...
98 views

(FEM) Reorder nodes or use sparse matrix storing techniques

Is it necessary to reorder nodes (using Reverse Cuthill-Mckee algorithm, for example) if I am already using a CSR or CSC storing technique? Because, since CSR/CSC only stores non-zero elements I guess ...
54 views

Problem of multiplication of big (sparse) matrix with numpy (python)

I wanted to multiply two simple (big and sparse) matrix with numpy. And I saw that the calculation fails when matrices are too big. If i take $X$ a random vector (size $n$). With pandas, I ...
36 views

Solver for generalized eigenvalue problem with multipoint constraints

We have the following generalized eigenvalue (set of) problem(s) $$[K_R(\kappa)]\{u_R\} = \omega^2[M_R(\kappa)]\{u_R\}\quad \forall \kappa \in [\kappa_0, \kappa_1]$$ with \begin{align} &K_R(\...
63 views

Numerical analysis, pivoting and incomplete LU decomposition

When doing LU decomposition, the algorithm will break down if any of the diagonal element $x_{ii}$ is zero. Therefore, we can use pivoting on the matrix such that $x_{ii}$ is no longer zero. That is ...
85 views

Minimize a function with sparse Hessian

The problem I am trying to solve involves minimising a function with respect to a large number (probably 10,000+) of parameters. I can cheaply compute both its Jacobian and its Hessian. The Hessian is ...
448 views

Which C++ linear algebra library is probably the fastest on solving huge sparse [square matrix] linear system?

I am developing a 2D CFD solver for fluid-particle interaction. To solve Navier-Stokes equations on a grid of size $10000\times 10000$ cells (or >1 million cells), a large linear system $Ax=b$ with $A$...
184 views

C standard for computational science

Which C standard should be used for computational science code ? Should we keep compatibility with C89/90/ANSI or jump to C99 or C11 ? Context: Code will use third-party : BLAS, LAPACK, MKL, ...
106 views

Memory and time requirements of the scipy sparse spsolve

I have a system of fairly large set of linear equations (approximately 30K equations). I am using scipy.sparse.spsolve to solve these equations. Initially, I tried ...
80 views

Why the MIRACLE of Lanczos/CG-like?

Lanczos/Arnoldi/Rietz/CG-like algorithm share the same core strategy... In each, a little miracle appears, most of the Gram-Schmidt inner products are zeroes! In others words, new direction need only ...
70 views

Fast calculation of $A^T B$

I need to compute a matrix-matrix product, $A^T B$, where $A$ is $n \times r$ sparse, and $B$ is $n \times q$ dense. The number of rows $n$ is far larger than both $r$ and $q$. In fact $n$ is so large ...
138 views

Integer operations vs floating point operations

I have been working with an algorithm, which uses additions of floating point vectors, (sparse matrix of floats)x(dense vector of floats) dot products I recently found out that I can get the same ...
424 views

Rule of thumb for sparse vs dense matrix storage

Suppose I know the expected sparsity of a matrix (i.e. the number of non-zeros / total possible number of non-zeros). Is there a rule of thumb (perhaps approximate) for deciding whether to use sparse ...
162 views

Moore-Penrose pseudoinverse of singular rank degenerate matrix

I am trying to attain the Moore-Penrose pseudoinverse of a very large, very sparse, rank-degenerate, singular, and square matrix. ($75000 \times 75000$, near rank). The matrix is a graph Laplacian and ...
104 views

Which SciPy nonlinear solver when Jacobian is analytically known and sparse?

I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ...
71 views

711 views

How can I speed up this code for sparse matrix-vector multiplication?

I've written a C++ function that multiplies a sparse matrix (stored in CSR format) by a dense vector. Here's the code: ...
150 views

Data structure for efficient high dimensional histogramming

What data structure (or C++ library implementing it) is most suitable for efficient high dimensional histogramming? I have an application where I need to compute something similar to a histogram in a ...
80 views

How to construct a eigensolver targeting a specific type of matrix

I need to diagonalize such kind of matrix during research: it's n-by-n, with it's upper-left (n-1)-by-(n-1) corner be diagonal while the nth row & column are dense. It's observed that the self ...
186 views

Leveraging scipy for matrix free finite elements

This will be a very general question. I have a 3D finite element code in Python which I would like to extend to handle "large" problems (~10^8 unknowns in the global system). Right now I am using the ...
74 views

How to do matrix operations with this way of storing sparse matrices

I read the way of storing the five or seven point laplace matrix for some poisson problem but I don't understand how can i multiply, add and subtract this stored sparse matrix by a vector or another ...