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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[].

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1answer
273 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 ...
9
votes
1answer
186 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
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1answer
140 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
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0answers
34 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
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2answers
289 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
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1answer
127 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 ...
50
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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
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1answer
75 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
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1answer
70 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
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1answer
139 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
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1answer
63 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
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0answers
442 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 ...
0
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1answer
56 views

Matrix manipulation instead of loops

I have the following matrix form $[J]$: $$ \begin{bmatrix} \{ v[3],p + v[2]\}\\ \{v[3], p + v[2], 2 p + v[1]\} \\ \{v[3], p + v[2],2 p + v[1], 3 p + v[0]\}\\ \{...
0
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0answers
38 views

3D Sparse array [duplicate]

Following the 3D matrix representation shown here Vitaliy Kaurov's answer for "Plot 3D boolean Array or matrix in Mathematica" Is it possible to use a SparseArray ...
7
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3answers
264 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 ...
3
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0answers
41 views

NetTrain doesn't accept sparse input?

The following code fails to execute: ...
11
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3answers
321 views

Most efficient way to build block / banded SparseArray

I have a matrix that I generate with a procedure that looks like this: ...
4
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3answers
96 views

efficient replacing of certain diagonal parts of array/matrix

in writing some code for FEM i need an efficient way to replace parts of the diagonal of a sparse array. Certain positions in the diagonal of the array (given in a list) should be changed to "1". An ...
3
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4answers
200 views

Creating large matrices from sub blocks

I am trying to generate a matrix from square blocks. Effectively, I have three blocks, call them $A_{diag}$, $A_{up}$, $A_{down}$, and a block of zeroes, which I'll just call $0$. I have some integer $...
11
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1answer
115 views

What are valid settings for the TreatRepeatedEntries sparse array option?

There is a system option that controls how to build sparse arrays when a position is assigned more than one value. The default setting is First, meaning that all ...
4
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1answer
126 views

Partitioning a sparse matrix into sparse sub-matrices

Given a normal matrix, for example m = Array[a,{4,4}] which has dimensions {4,4}, I can partition it by using: ...
5
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0answers
104 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 ...
4
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1answer
535 views

Using dense matrix is faster than sparse matrix in LinearSolve [closed]

I'm doing FEM with Mathematica and have to deal with LinearSolve of a large matrix inside a Newton loop constantly. Hence I need to speed up the computation efficiency of LinearSolve. I'm aware of ...
11
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3answers
444 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 ...
7
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0answers
76 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 ...
1
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0answers
32 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 ...
3
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0answers
68 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. ...
4
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0answers
65 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 ...
0
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0answers
288 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 ...
2
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3answers
156 views

How I can generate a matrix from a set of terms?

I want to build a matrix, from the following set $S = \{a b , a c\}$ S = {a b , a c} where the terms of S represent the raw of the matrix ...
0
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0answers
141 views

Find Eigenvalues close to a Target for a Generalised Eigenvalue problem of the type Ax=λBx with A and B very sparse

So I have been using Mathematica as a tool to discretise large linear systems of PDEs and cast them as algebraic eigenvalue problems involving very large sparse matrices. These are usually complex and ...
6
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1answer
212 views

Why does SparseArray allow some patterns but not others?

When building a SparseArray, patterns of the form {i_, i_} and {i_, j_} are fine, but ...
6
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2answers
118 views

Using sparse matrices when value depends on position

I am working with solving a linear system that becomes a tridiagonal matrix. In order to speed up the process for large matrices, I want to use sparse matrices. My problem is that the values are not ...
3
votes
3answers
861 views

How to create a lists of matrices?

I would like to creat a list of matrices from the following rules: 1- All matrices of the list have diagonal equal to zero. 2- The first matrix have 2x2 dimension, ...
2
votes
2answers
141 views

Creating a list of arrays according to given rules

I want to create a list of matrices from the following rules: All matrices of the list have diagonal equal to zero. The first element of the list is a 2x2 matrix, having elements are given by ...
0
votes
1answer
105 views

Parse large ASCII matrix

I am parsing a large ASCII sparse matrix, output of PETSc, but my current implementation is impossibly slow. I don't know how I could speed that up. The ASCII file of a sparse PETSc ...
3
votes
1answer
252 views

Problems with RandomChoice

Consider an Matrix of dimension n1xn1. I would like to get a list with n2 distinct matrix (of dimension ...
6
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2answers
219 views

Why the sparse array is ill-conditioned?

Bug introduced in 8.0 or earlier and persisting through 11.1.0 or later Given that I have a knot vector $\mathbf U$ and a set of parameter values $\mathbf T$: ...
2
votes
1answer
145 views

Build sparse matrix in mathematica knowing position i,j and value to store, from file

I have a file formatted in this way: Row Column Value i j Vij i= INT Number row where in sparse matrix I want the ...
3
votes
2answers
164 views

Merging SparseArrays (or normal arrays)

I have a list of SparseArrays, and I want to combine them into one array that concatenates their rules. I don't want to connect them together like ...
6
votes
1answer
145 views

Multiplying SparseArray by negative number Crashes Kernel

Bug introduced in 9.0 and persisting through 11.0 Can anyone reproduce the following bug, or figure out a work-around. The following crashes the kernel on both Mathematica 10 and 11, on my macs, ...
6
votes
1answer
129 views

Nonsparse SparseArray crashes the Kernel

Bug introduced in 10.0 and fixed in 11.1 On Windows 10, 64 bit, version 11.0.1, my kernel just started crashing for no reason as for as I can see. Does/should the following crash your kernel? ...
3
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0answers
53 views

Map entries of StructuredArray

I have the following defintion arr = SymmetrizedArray[{1, 2} -> 1, {4, 4}, Antisymmetric[{1, 2}]] which gives a ...
0
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0answers
50 views

How to modify the default value of a `SparseArray` without intermediate non sparse matrices [duplicate]

How to modify the default value of a SparseArray? All of my ideas doesn't work, because of the ReadProtected attribute. Is there ...
6
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2answers
216 views

directly change the background value of a SparseArray?

given a SparseArray s = SparseArray[{1, 10} -> 1, {1, 10}, a] I can extract the background value (see What are SparseArray ...
7
votes
1answer
206 views

Bug? Strange behaviour of FullSimplify when checking an equality of SparseArray's

Edit (15 Dec '16): bug noticed in v11.0 and reported as CASE:3796403. Edit (03 May '17): bug fixed in v11.1 (verified in v11.1.1). I stumbled upon the following strange behaviour. Disclaimer: I ...
7
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4answers
405 views

How to find position where a sequence drops off to zero

Suppose I have a sequence seq = {0,0,0,1,2,3,1,0,0,0,4,5,8,0} and I want to find the first position after which the sequence drops to zero (which in this case, is ...
0
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1answer
211 views

How to build a histogram from the mean of 100 matrices

I have a matrix that looks like this: ...
0
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0answers
28 views

Sparse (Weighted) Adjacency Matrix & SparseArray: encoding multiple weights at a given edge [duplicate]

Context Below is just an arbitrary example. It is not perfect, but hopefully it serves the point of what I would like to accomplish. Say you have a sparse adjacency matrix, $\bf{A}$, where a value ...
2
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1answer
85 views

How to fill in matrices by enforcing a condition on each entry quickly?

In the process of solving a 3D time-dependent PDE, I need to fill several matrices which their sizes are quite high. These matrices are constructed based on the radii of the mesh nodes in the 3 ...