# 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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### Solving 2D Poisson Eq with mixed BC's in Python

I am trying to numerically solve the Poisson's equation $$u_{xx} + u_{yy} = - \cos(x) \quad \text{if} - \pi/2 \leq x \leq \pi/2 \quad \text{0 otherwise}$$ The domain is the rectangle with vertices ...
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### How can I extract the banded or block diagonal part of a sparse matrix in MATLAB?

Given a large sparse (square) matrix in MATLAB, how can I extract the banded or the block-diagonal parts (of fixed size) of it efficiently? These are useful operations when prototyping and testing ...
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### Solving PDEs: What is the best way to deal with non-banded/dense jacobians?

I have a system of PDEs describing atmospheric chemistry and transport. I use finite-differences to make my system of PDEs into a system of ~10,000 ODEs. I then integrate the ODEs forward in time with ...
174 views

### eigsh (Lanczos algorithm) slows down for degenerate eigenvalues

I have a complex Hermitian matrix of size about $70000\times 70000$. I want about 100 eigenvalues near 0. However, I know that every eigenvalues are two-fold degenerate. I found out that the running ...
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1 vote
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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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### Does shift-invert method has invertibility issue?

Please note that I have nearly zero background on numerical methods. I understand the shift invert method as described in SciPy Tutorial The main argument of the above link is as follows. Suppose we ...
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### 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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### 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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1 vote
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### 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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1 vote
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### 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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### 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, ...
1 vote
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### 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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### 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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### 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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1 vote
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### 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 ...
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### 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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1 vote
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### 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 ...
155 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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### 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 $n\times n$ matrix $A$ with a pretty interesting structure. It has a block structure with a symmetric structure but asymmetric blocks. Expressed mathematically the block \$A_{jk} = A_{...
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