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Questions tagged [sparse-arrays]

Questions on the construction and manipulation of sparse arrays in Mathematica, with functions like SparseArray[] and Band[].

10
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3answers
480 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
80 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
20 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
48 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 ...
15
votes
0answers
417 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 ...
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 ...
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 ...
7
votes
1answer
167 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
5answers
462 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
795 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
593 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^...
5
votes
1answer
222 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
112 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
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 ...
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
201 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}{\...
4
votes
1answer
320 views

How to accelerate updating some parts of sparse matrices?

I am trying to update some parts of an specific matrix as rapidly as possible. In what follows, I first set up the basics things that I want to use ...
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
127 views

Delete zeros from a sparse array [duplicate]

Why doesn't SparseArray automatically remove zero entries? The code ...
1
vote
2answers
58 views
4
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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 ...
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 ...
9
votes
1answer
261 views

Calculating the rank of a huge sparse array

By virtue of the suggestion in my previous question, I constructed the sparse matrix whose size is $518400 \times 86400$, mostly filled with $0$ and $\pm 1$. Now I want to calculate its rank. Since <...
9
votes
5answers
433 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: ...
2
votes
1answer
59 views
1
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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}\...
21
votes
3answers
4k views

Find the eigenvector associated with the smallest eigenvalue, not smallest in magnitude

I am trying to find the eigenvector of a $20000 \times 20000$ sparse matrix associated with the smallest eigenvalue. I realized that the smallest eigenvalue might be negative; for example, if the ...
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. ...
3
votes
0answers
65 views

Trying to create rank-1 SparseArray through LibraryLink causes crash

Bug introduced in 10.0 or earlier and fixed in 11.3 When I try to create a 2D SparseArray through LibraryLink's MSparseArray_fromExplicitPositions, it works fine. ...
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 ...
7
votes
3answers
256 views

Generating a (sparse?) array from data

I have a list: {{pos_1,val_1},{pos_2,val_2},...} and would like to generate an array of dimension d, with values ...
1
vote
1answer
109 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 ...
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
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. ...
11
votes
3answers
429 views

Why can't I reshape to any dimensions?

Bug introduced in 11.0 and fixed in 11.3.0 I am trying to reshape a $2 \times 2 \times 2$ array into a $n \times m$ array. It seems that if the matrix is defined via ...
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 ...
7
votes
3answers
511 views

Nonzero element positions of a matrix

Let m={{1, 2, 0}, {4, 0, 9}}; I want to find the position of every nonzero element of the above matrix. The code ...
5
votes
2answers
333 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
105 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 ...
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
93 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
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"] ...
1
vote
1answer
218 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 ...
2
votes
1answer
123 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....
4
votes
1answer
126 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 ...