# Questions tagged [sparse-arrays]

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

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### LinearSolve and Krylov Method options

I need to solve a large, sparse, linear system. At some point Method -> "Multifrontal" fails and a bit later also "Pardiso" ...
174 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 ...
197 views

### Bug in PositiveDefiniteMatrixQ?

Fixed in 10.1.0. Exists in at least 9.0.1 -- 10.0.2. This seems like a bug in PositiveDefiniteMatrixQ to me: ...
89 views

### LibraryLink: Create SparseArray directly from row pointers and column indices

In Mathematica, sparse arrays use a CSR representation. Suppose I already have data in this format. Is there a way to create an MSparseArray from it directly with ...
79 views

### Memory usage for smallest eigenvalues

I have a bunch of hermitian matrices which are huge (of order 2^17 x 2^17) but extremely sparse so that, when I build the matrices, the usage of RAM is low (say of order 1 GB or similar). The ...
119 views

### Reproducible kernel crash using Eigensystem with Arnoldi on SparseArray

Using Arnoldi method to find some eigenvalues (say 20), with shift value taken in the middle of the spectrum, of a large sparse matrix the Kernel crashes with no error returned. The crash occurs if ...
81 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. ...
70 views

### ParametricNDSolveValue with SparseArrays

I want to solve large, sparse matrix systems with ParametricNDSolveValue and was hoping to use SparseArray to speed up the computation. However I find that ParametricNDSolveValue doesn't seem to work ...
182 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 ...
49 views

### NetTrain doesn't accept sparse input?

The following code fails to execute: ...
72 views

### Why is SparseArray atomic?

This answer tells us that functions like ReplaceAll do not straightforwardly work for the entries of sparse arrays because a ...
92 views

### Why isn't SparseArray working in this case?

This works: SparseArray[{{1, 1} -> 1, {2, 2} -> 2}]\ (* {{1, 0}, {0, 2}} *) This works: ...
616 views

### Finding eigenvalues in Mathematica: why so slow?

I am trying to find the eigensystem of a large sparse real symmetric matrix, and I only need the lowest 40 or so eigenstates. The relevant code is as follows: ...
483 views

### How can I force the use of sparse diagonalization methods?

When I evaluate the Eigenvalues function on a very large (e.g. 2^16 x 2^16) sparse matrix, Mathematica says something like: Because finding 65536 out of the ...
177 views

### Efficient storage of Kronecker sum of circulant matrices+diagonal matrix

I have a square matrix of the form $$M=D+\overset{N}{\underset{n=1}\bigoplus}R_n,$$ where $R_n$ are circulant matrices, $D$ is a diagonal matrix and $\oplus$ is Kronecker sum. Its size is quite big, ...
368 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 ...
54 views

### Map entries of StructuredArray

I have the following defintion arr = SymmetrizedArray[{1, 2} -> 1, {4, 4}, Antisymmetric[{1, 2}]] which gives a ...
114 views

### Det and MatrixRank freezes on SparseArray with nonzero default value

Bug introduced in 7.0 or earlier and fixed in 9.0.1 or earlier Why does the following simple code never come to an end (at least with version 8) ...
87 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 ...
37 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 <...
38 views

### Is it safe to change MSparseArrays which lack column indices?

I am using sparse arrays with LibraryLink. I noticed that when MSparseArray_fromExplicitPositions and MSparseArray_fromMTensor ...
116 views

### How to speed up summing a large number of vectors

First let me explain what I am trying to do in my code. Assume that I send a very short chirp (2,000 ms long) into a domain filled with 20,000 particles randomly scattered in the domain. The ...
407 views

### Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
199 views

### Memory used by SparseArray objects

In dealing with a quantum mechanics problem, I am representing some many-body states in two different ways in Mathematica. For two parameters n and ...
461 views

### The Jacobi-Davidson method

Does any implementation of the Jacobi-Davidson method for Mathematica exist? A highly parallelized version for sparse matrices would be of special interest.
48 views

### How to apply PolynomialMod to a SparseArray?

I have a list bdrs of SparseArrays, whose entries are polynomials in the variable t with ...
68 views

### Why did LinearSolve give me two different results?

Given that I have a sparse array as follows: ...
30 views

### Computing the invariant factors of a sparse matrix

Let M be a sparse $n\times m$ integral matrix, where $nm$ is very large. The goal is to compute its invariant factors. The naïve approach ...
377 views

### Inverse of a sparse 21x21 symbolic matrix

I am trying to compute the inverse of the following symmetric sparse(density 0.37) 21x21 matrix involving symbolic expressions in the entries(the variables ...
46 views