Questions tagged [sparse-arrays]
Questions on the construction and manipulation of sparse arrays in Mathematica, with functions like SparseArray[] and Band[].
222 questions
12
votes
1answer
157 views
+500
Generate coefficient array from general formula of linear equation system
This is a problem coming out in the implementation of finite difference method (FDM).
Here is a toy example. Suppose we want to solve the boundary value problem (BVP)
$$y''(x)=\sin(x),\ y(0)=0,\ y(...
10
votes
3answers
518 views
Optimising subdiagonal shift matrix generation time
I want a square matrix $A$ such that $$A_{i,i-1} = 1 \ \forall i\\ A_{i,j} = 0 \text{ for } \ j \ne i-1$$
I have tried
...
5
votes
2answers
87 views
Lowest Magnitude Eigenvalues of Large Sparse Matrices
I am trying to find the first three lowest eigenvalues of large sparse matrices of size range $10^3 - 10^5$. The matrices depend on some parameter $x$, so I first construct the matrices and then use ...
0
votes
0answers
22 views
Inverse of Sparse Diagonal Array not Sparse
Kind of bummed that when I take the inverse of a matrix that is a diagonal sparse array, the result in not a sparse array. Further, the time to compute the inverse is the same as the time to compute ...
0
votes
1answer
49 views
Time used by Mathematica to calculate tridiagonal matrix
I have a question.
I need to find the eigenvalues and eigenvectors of a tridiagonal matrix of size NxN. Can you tell me how much time does Mathematica need to do that in minutes? for
Size N ...
4
votes
5answers
465 views
How to generate binary array whose elements with values 1 are randomly drawn
I am trying to generate a binary matrix (whose elements are 0 or 1) of dimension 20x20. To do this, I want to supply as input the number of matrix elements that will take value 1. After, I want to ...
12
votes
2answers
799 views
Solving “Resistance between two nodes on a grid” problem in Mathematica
In the context of resistor networks and finding the (equivalent) resistance between two arbitrary nodes, I am trying to learn how to write
a generic approach in Mathematica, generic as in an approach ...
9
votes
2answers
603 views
Quickly creating a sparse array
The motivation for my question is that I'm creating very large, very sparse symmetric matrices and finding the largest eigenvalue. (Think upwards of $10^5\times 10^5$ size matrices, with at most $10^...
0
votes
0answers
32 views
Selecting some vectors from a matrix
I am trying to write a code for band matrices that store only the nonzero vectors. For example if I have tridiagonal matrix of size 10, I want to store only the three diagonals as a vectors. n here ...
11
votes
4answers
754 views
8
votes
0answers
87 views
Matrix-free Arnoldi method for eigensystems
I am solving a generalized eigenvalue problem
$$\mathbf S\,\mathbf x = \lambda\,\mathbf M\,\mathbf x$$
w/ $\mathbf S := \mathbf B\,\mathbf A^{-1}\,\mathbf B^{T}$, and $\mathbf A$ is a sparse ...
1
vote
1answer
214 views
Bottom-most left-most entries in a sparse array
I have a list bdrs of SparseArrays, which represent the boundary matrices of a chain complex $R^{d_0}\overset{\partial_1}{\...
2
votes
1answer
114 views
Indices of nonzero rows in a sparse array
Given $A\!\in\!\mathbb{Z}^{m\times n}$ stored as a=SparseArray[{...},{m,n}], how can I obtain the list of all indices $i\!\in\!\{1,\ldots,m\}$ for which the $i$-th ...
0
votes
1answer
58 views
Read text files as sparse arrays and concatenate in a loop
I would like to read multiple text files and build a sparse array by concatenating row-wise one after the other. The text files are ordered in the following format:
\begin{matrix}
0, & 0, &...
4
votes
1answer
133 views
Delete zeros from a sparse array [duplicate]
Why doesn't SparseArray automatically remove zero entries? The code
...
1
vote
2answers
58 views
1
vote
1answer
23 views
4
votes
3answers
289 views
Sparsity of a sparse array without converting it to a regular one
My goal is to find such properties of a sparse matrix as the maximum/average number of non-zero elements per row.
The brute-force way of doing this is via converting the sparse array into a regular ...
31
votes
1answer
1k views
Wrong eigenvalues from a sparse matrix: eigenvalues are nonreal
Bug introduced in 9.0 or earlier and persisting through 12.0.
I notice in the following example that wrong complex eigenvalues are resulted if calculating from a Hermitian sparse matrix, which should ...
2
votes
0answers
55 views
How to construct a time-dependent matrix quickly?
In the process of discretization of a 4D PDE, I need to construct a final sparse matrix $B$, which is very large (I denoted by $\text{size}$ here) and time-dependent, viz, some of its entries change ...
5
votes
1answer
224 views
Parallelize the construction of sparse matrices
I'm trying to parallelize a few constructions of chain complexes (given as a list of sparse matrices). I have a function that for any column (or row) computes the list of nonzero entries in that ...
2
votes
1answer
59 views
1
vote
1answer
46 views
Speed up construction of large matrix with if statements
I am constructing a matrix of the form
$$
T_{i_aj_ak_al_a,i_bj_bk_bl_b} = T_{i_ai_b}\delta_{j_aj_b}\delta_{k_ak_b}\delta_{l_al_b} + T_{j_aj_b}\delta_{i_ai_b}\delta_{k_ak_b}\delta_{l_al_b} + T_{k_ak_b}\...
0
votes
0answers
29 views
How to add the duplicated positions in sparse array? [duplicate]
When we use the SparseArray in such form:
SparseArray[{pos1,pos2}->{val}]
We know that we don't have duplication of positions in pos1 and pos2. I mean that we ...
3
votes
2answers
46 views
Using elements of a list as SparseArray patterns: “can't be used as part specification”
I don't have much experience with SparseArray, and the search here did not give me an answer to this.
I'm trying to numerically compute a certain spectrum, and the ...
0
votes
0answers
26 views
SparseArray with width or height 0
I can store the zero matrix (=module morphism) $R^2\overset{a}{\leftarrow} R^3$ as a=SparseArray[{},{2,3}]. But
$R^0\overset{a}{\leftarrow} R^3$ stored as ...
1
vote
1answer
110 views
Sparse matrices dot multiplication
I have two huge sparse matrices, and I am interested in dot multiplication them. But I have a memory issue so a notebook is a shutdown. I am using the 11.3 version.
Any suggestion on how to avoid ...
1
vote
2answers
78 views
Filtering sparse matrix
I am interested in filtering a sparse matrix, where the values are between zero and one. I do it in the following manner.
...
4
votes
0answers
168 views
Loopy Belief Propagation
I look for an efficient way to implement a Belief Propagation in Pairwise Markov Random Field.
Each node is a binary random variable, and the unary potential function is
...
2
votes
1answer
82 views
Save a list as a value in the sparse matrix
I am interested in save a list (the size of the list is two) of numbers in the sparse matrix, but this is not supported.
Maybe you familiar with some workarounds or any suggestion on another data ...
5
votes
2answers
337 views
Replace values in sparse matrix
I am interested in updating the values of the sparse matrix. I have a list of matrix element which I am interested in updating and a list of new values. Currently, I do it in the following manner:
<...
1
vote
1answer
107 views
SparseArray: accesing nonzero row and column entries
I have an enormous $m\!\times\!n$ sparse matrix $d$ with $l$ nonzero entries, stored as d=SparseArray[{{i1,j1}->w1,...,{il,jl}->wl},{m,n}];.
How do I access ...
9
votes
5answers
435 views
Replace diagonal elements in sparse matrix
I am interested in replacing all elements in a diagonal of a sparse matrix with zero. Currently, I do it in the following manner:
...
6
votes
1answer
356 views
How to find k largest element and their position in a matrix?
I have a sparse matrix, and I am interested in find k largest elements and their positions in the matrix.
I do it in the following manner:
...
1
vote
1answer
94 views
Optimization of a slow function - reason to why it is slow
Edit:
Okay, my question was viewed quite a few times but not answered so I assume I phrased/presented in a confusing way. I'll try to rephrase my problem to make it more accessible because luckily I ...
6
votes
1answer
103 views
Efficiently fill sparse matrix involving BSpline
Context
In order to implement regularised fitting in 2 or 3 dimensions (as is done say here) using BSplineBasis one needs to evaluate a basis over a set of data.
...
6
votes
1answer
64 views
How to prevent a SparseArray entry from being specified when it coincides with the default value?
Mathematica doesn't notice when an entry coincides with the default value:
(IdentityMatrix[2, SparseArray] - IdentityMatrix[2, SparseArray])["NonzeroPositions"]
...
2
votes
1answer
126 views
How do I dynamically update a SparseArray?
Say I have a "seed" SparseArray e.g. m=SparseArray[{1->1}]. How do I add a rule at a position that has not yet been defined e....
1
vote
1answer
224 views
Find a few eigenvalues of a HUGE sparse Hermitian matrix
I know that methods such as Arnoldi and FEAST can be employed to only find a few eigenvalues. But now I need to add another ...
7
votes
1answer
170 views
Fast way to reassemble SparseArrays
I often have to deal with nonlinear shape optimization problems involving curves or surfaces surfaces. A classical example is Plateau's problem.
No matter if I use gradient-based techniques (such as ...
4
votes
1answer
129 views
Reorder matrix for nested dissection
I'm implementing a nested dissection linear solver outside of Mathematica and my original data is actually a graph, from which I have to construct an appropriate adjacency matrix to feed into the ...
2
votes
0answers
30 views
Odd behavior of ArrayReshape with SparseArrays
I am trying to understand why I am seeing inconsistent results when using ArrayReshape on a SparseArray vs. a normal nested <...
4
votes
2answers
281 views
Sparse block matrices all wrong
I need to represent $M-\lambda\cdot\textrm{Identity}$ where $M$ is an operator on $V_1\oplus\cdots\oplus V_n$ made from
$$
V_1\xrightarrow{M_1}V_2\xrightarrow{M_2}\cdots\xrightarrow{M_{n-1}}V_n\...
4
votes
1answer
122 views
Generalized linear algebraic equation solver
$\newcommand{\d}{\vec{d}}$
$\newcommand{\S}{\vec{S}}$
In Mathematica one can easily solve a linear system given by
$$A \vec{S} = \vec{d}$$
where $A$ is a matrix, simply by using
...
48
votes
2answers
1k views
A geometric multigrid solver for Mathematica?
Cross posted to community.wolfram.com
Mathematica ships a variety of linear solvers through the interface
LinearSolve[A, b, Method -> method]
the most ...
3
votes
1answer
65 views
Memory issue of SparseArray between Notebook window and Wolfram Documentation window
Recently I'm trying creating a 80000 x 80000 sparse array in Mathematica, and I discovered a strange thing when using SparseArray[].
Code: ...
5
votes
1answer
67 views
Fastest way to drop multiple rows and columns from SparseArrays
I would like to prune some unimportant rows and columns from a SparseArray to accelerate solving some eigenvalue problems.
Given
...
5
votes
1answer
138 views
How to speed up working with Sparse Arrays
I make a SparseArray and then modify it by adding rows together. This seems to take a long time. Can it be speeded up?
...
4
votes
1answer
52 views
control symmetry property when exporting matrix as Matrix Market format .mtx
For example, I have
h = SparseArray@{{0, I}, {-I, 0}}
If I export h as matrix market format(.mtx) like
...
15
votes
0answers
424 views
Wrong eigenvalues from a sparse matrix
Bug introduced after 5.0, in or before 8.0 and persisting through 12.0.
I notice in the following example that wrong smallest 2 eigenvalues are resulted if calculating from a sparse matrix. But it ...
