Questions tagged [sparse-matrix]

Questions related to storage, assembly, operations, and other aspects of dealing with sparse matrices, for which only non-zero elements are stored. Questions that do not with sparse matrices directly, but other means of using sparsity should be tagged with [sparse-operator].

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59 views

Software for solving large systems of linear equations over gf(2)

What available solvers are there for linear equation solver over GF(2) (Boolean), capable of dealing with large sparse systems (in the 10k - 100k variables range)?
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3answers
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How to apply the boundary condition when global stiffness matrix is stored in csr format? [duplicate]

I am solving the poisson equation and I constructed the global stiffness matrix in compressed row storage format. Then I wrote the preconditioned conjugate gradient solver for solving the system of ...
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72 views

C.S.R method in finite element matrix assembly

I have solved the 2D Poisson equation using finite element method with simplex triangular element in MATLAB. First, I generated the triangular mesh using pdetool in ...
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49 views

Nonsymmetric permutations for LU factorisation of symmetric matrix

Let $A$ be a symmetric matrix. It is then well known that computing the LU factorisation of $PAP^T$ instead of $A$ for a suitably chosen permutation matrix $P$ can greatly reduce fill-in. My question ...
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1answer
57 views

Nonlinear root solving libraries which accept a Jacobian in band-storage

I'm in search for a library for solving large systems of non-linear equations, similar to MINPACK, but unlike MINPACK, can accept a Jacobian in band-storage. My Jacobian is sometimes not invertible, ...
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2answers
129 views

Solving a specific sparse linear system without dense materialization

I need to (computationally) solve a system of equations, for the purposes of an interior point method, of the form $$ \left[\begin{array}{cc}B & A^T \\ A & 0\end{array}\right] \left[\begin{...
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1answer
568 views

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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1answer
213 views

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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1answer
99 views

Complexity of solving an image differential linear system

Define an "image differential linear system" as a linear system $A\mathbf{x}=\mathbf{b}$ wherein $\mathbf{x}$ contains the ($\mathbb{R}$) pixels of an image and each row of $A$ constrains ...
6
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1answer
179 views

Parallelize Scipy iterative methods for linear equation systems(bicgstab) in Python

I need to solve linear equations system Ax = b, where A is a sparse CSR matrix with size 500 000 x 500 000. I'am using scipy.bicgstab and it takes almost 10min to solve this system on my PC and I need ...
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56 views

performance comparison between PETSc and SLATE

We want to start a new project to solve a large-scale inverse problem (O(10^6) number of parameters) to invert for subsurface wave speeds. We will use FEM to solve forward and adjoint PDEs. In our ...
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62 views

How to make a directed graph symmetric?

Say I have a directed graph given as an adjacency matrix $A$ in CSR format represented by the arrays ia (row indexes) and ja (...
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1answer
32 views

In Eigen, can a sparse matrix contain vectors/objects instead of simple scalar values?

I need to have a sparse matrix whose elements are not simple numbers, but objects, e.g. a couple of floating point values and a bunch of integer indices. I am wondering if Eigen has something similar, ...
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Choice of iterative solver for a sparse asymmetric matrix with symmetric structure

I have a sparse $nxn$ matrix A with pretty interesting structure. It has a block structure with symmetric structure but asymmetric blocks. Expressed mathematically $A_{jk} = A_{kj}$ but $A_{jk} \neq ...
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3answers
111 views

Create a sparse matrix

I am writing a FE program which calculates the displacements under a uniform load. I want to store the stiffness matrix in sparse form(COO) without using an external library.Assume an upper-bound for ...
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2answers
127 views

L1 least squares minimization with a sparse matrix

I have the following problem: $$\min_{x\in \mathbb{R}^n}\|Ax-b\|_1$$ where the matrix $A$ is large and sparse. I am looking for methods/code that can minimize this efficiently. References are very ...
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2answers
239 views

When is it easy to invert a sparse matrix?

(Crossposted on cstheory.SE) When is it easy to invert a sparse matrix? Specifically, I'm wondering about the cases in which matrix inversion has similar cost to sparse matrix multiplication, hence ...
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3answers
277 views

On the reordering of sparse matrices

I have been reading on different techniques used to reorder sparse matrices to achieve better performance, the most popular being the Cuthill-McKee or Reverse Cuthill-McKee algorithm. Most of those ...
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71 views

Derivative-free ill-conditioned non-linear least squares

I am looking for a package which can solve (non-linear) least squares problems without the use of derivatives (because of an expensive model), but which also deals with ill-conditioning well (such as ...
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1answer
132 views

Implementation of sparse matrix SVD for GPU

I have a sparse matrix $W$ which is almost-squared ($N+1 \times N$) and I would like to know the eigenvalues of $A = W^T W$. $A$ is Hermitian so the eigenvalues are real-positive valued. The usual ...
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1answer
113 views

Solving large sparse system

I am working on a problem with very large sparse matrices. I'd like to compute $A^{-1} B$, that is a crucial part of converting DAE to ODE (and there is no workaround). Here size of $A$ is 2E+5 x 2E+5 ...
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1answer
147 views

Efficient way to solve a set of linear equations $Ax=b$ when $A$ is sparse and some elements of $b$ are equal to zero

I have a set of linear equations, $Ax=b$. And about half of the elements in the right-hand side (vector $b$) are equal to zero. My system matrix $A$ is a sparse complex matrix. And $A$ is in the size ...
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2answers
296 views

Is there an iterative solver for dense matrices with possible zero diagonal entries?

Is there an iterative solver that can handle potentially zero entries on the central diagonal? I am implementing a polynomial fitting algorithm (up to $10^{th}$-order) and my matrix is a "...
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0answers
130 views

Compute Nullspace of Sparse Matrix

I am computing the nullspace of a sparse rectangular $m$ x $n$ matrix $A$, where $m$ << $n$. I do this by computing the QR decomposition of $A^T$ and extract the $n-m$ right-most columns of the ...
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1answer
95 views

Solving a sparse linear system using transpose of lower triangular matrix without copying

I have a sparse lower-triangular matrix $L$, and a right-hand side $b$, and I'd like to solve the linear system $$L^T x = b$$ but without explicitly creating $L^T$. Ideally, I could write something ...
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1answer
87 views

Fast way to build stiffness directly as CSC matrix

I have been working on finite element code in Fortran 2008, and have implemented my own sparse matrix types. I have found that mapping local stiffness matrices (real type) to a global COO sparse type ...
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1answer
67 views

How to delete $n^{th}$ row and $n^{th}$ column of a matrix K in Petsc and restructure it?

I have a matrix K in Petsc. I want to delete the $n^{th}$ row and $n^{th}$ column of this matrix and restructure it. I am a beginner in Petsc. Can you suggest how to do it? Example: I have matrix K ...
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1answer
300 views

Why is 'scipy.sparse.linalg.spilu' less efficient than 'scipy.linalg.lu' for sparse matrix?

I have a matrix B which is sparse and try to utilize a function scipy.sparse.linalg.spilu specialized for sparse matrix to ...
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1answer
51 views

what does `cusparse<t>csrsv2_analysis()` do?

In cuSPARSE, you can solve a sparse triangular linear system by calling cusparse<t>csrsv2_solve(). However, you need to call ...
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1answer
146 views

Fast nonzero indices per row/column for (sparse) 2D numpy array

I am looking for the fastest way to obtain a list of the nonzero indices of a 2D array per row and per column. The following is a working piece of code: ...
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1answer
66 views

How to fill matrix entries for two-dimensional implicit finite-difference for the general case

If I have derived a finite-difference formula for a 2D problem, for example something like: $af_{i,j}+bf_{i-1,j}+cf_{i,j-1}+df_{i-1,j-1}=g_{i,j}$ where f is the unknown function on a grid and ...
2
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1answer
87 views

Best way to convert a sparse (containing zeros) covariance matrix into a correlation matrix?

I have a $100$x$100$ covariance matrix that looks like this. Some rows/cols are all-zero because those corresponding elements are not present in the sample from which covariance is calculated. I'm ...
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0answers
202 views

What is the algorithm to convert an adjacency matrix to a block diagonal structure?

I'm a little at loss as to what my supervisor meant by the "hierarchical block decomposition" of a matrix, but the goal is to put a sparse symmetric adjacency matrix into a block diagonal structure to ...
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0answers
56 views

How to determine the finite difference coefficient matrix in 2D with periodic BC?

I'm solving a PDE in matlab using ode15s, and since the spatial dimension is 2, and number of variables grow large very quickly, I need to supply the structure of ...
3
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1answer
344 views

Sparse Matrix Matrix multiplication using Intel MKL

Let $D$ be a sparse matrix. I want to compute $D\times D^T$. As $D$ is fairly large, so I am row-slicing $D$. That means for a range $(i,j)$, I am computing $C = D(i:j,:) \times D^T$ and performing ...
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0answers
101 views

What is the state-of-the-art in parallel sparse matrix and dense vector multiplication?

For sure, there has been many highly optimized library on this. But I am working on a matrix-free context since the problem size does not allow explicit storage of sparse matrix elements. I'd love ...
2
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1answer
148 views

Sparse matrix-matrix multiplication using AVX2

I have two sparse general matrices stored in CSR format I need to multiply. Is there any chance to gain performance using AVX2? In general the matrices are big (hundreds of millions of non-zeros and ...
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0answers
20 views

Barrier algorithm Gurobi and interior-point quadprog; what kind of matrices can it handle the best (sparse or dense, large or small problems)?

I am trying to solve a QP problem. Does anybody know the differences between the interior-point-convex algorithm of quadprog and the barrier method of Gurobi in terms which kind of matrices can the ...
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1answer
47 views

Matrix requirements for cusparse*csrgemm2

I would like to perform a matrix multiplication like: $C=A*B*A'$ using cusparse library function cusparseDcsrgemm2. To do this I split it into two matrix-matrix multiplications where all matrices ...
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2answers
95 views

CSC Sparse Matrices: Why sort row data for Ax=b problems?

I have a matrix in Coordinate format and I will convert it to CSC. As a reference, the format I am using looks like this, but I am not using the pointerE matrix, which I think is superfluous. My ...
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2answers
104 views

How to understand the storage of the Hessenberg matrix of Krylov subspace matrix?

For the Krylov subspace method to solve the large sparse linear system, we first need to generate a subspace Km = span{v,Av,...A^{m-1}v}, which indeed a process ...
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2answers
502 views

Inverting really big symmetric block diagonal matrix

I have a really big symmetric 7.000.000 X 7.000.000 matrix that i would like to invert. The matrix is extremely sparse and it can be rearranged as to become a block diagonal matrix. The biggest blocks ...
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0answers
60 views

Numerical methods. MDF (ILU) implementation

I am trying to implement Minimum Discarded Fill (MDF) Ordering algorithm for incomplete matrix factorization. The algorithm description is here on page 60 Preconditioning Techniques for a Newton–...
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0answers
29 views

Multibody Systems modeling disadvantages [closed]

Multibody Systems modeling is a very systematic approach usually results in large sparse Jacbian matrix. I am working to model a system consisting of 11 bodies and 63 constraint equations as soon as i ...
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2answers
202 views

Block-matrix: optimal fill-in reduction for LU factorization

Consider a square $N \times N$ block-matrix $\mathbf{A}$, where each $n \times n$ block $\mathbf{A}_{ii}$ is either a dense block or a zero-block. So, $N$ denotes the number of blocks, $n$ denotes the ...
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0answers
55 views

Fast algorithm for computing lower mode shapes and natural frequencies in MATLAB using sparse stiffness and mass matrices

I am looking for a fast algorithm for computing eigenvalues and eigenvectors from sparse stiffness and mass matrices in MATLAB. The eig(K, M) doesn't work with ...
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2answers
116 views

When should I write a matrix-vector function to handle the sparse matrix vector multiplication?

This semster, I have been studying the iterative methods for large sparse matrix system. But I have some questions. For large sparse matrix, we must use an economic storage to store them. The most ...
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1answer
121 views

What method to solve a sparse complex symmetric (non-Hermitian) system?

I have a sparse system (about 78% of zero entries) that is complex and symmetric (but not Hermitian). The following figure shows the structure of the problem. The off-diagonal blocks are incidence ...
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3answers
208 views

Is there any other sparse matrix data in matlab built-in file?

I want to do some numerical examples solving large sparse linear system Ax=b. And I want to use some data from Maltab itself because this experiments are easily ...
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0answers
107 views

understanding Domain Decomposition with example

I am new in Domain Decomposition method. I am started to solve $-\Delta u = f$ in $\Omega$ and $u = 0$ on $\partial\Omega$. From that I get in $\Omega _1$ $$\begin{bmatrix}4&-1\\-1&4\end{...

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