Questions tagged [sparse-arrays]
Questions on the construction and manipulation of sparse arrays in Mathematica, with functions like SparseArray[] and Band[].
243
questions
2
votes
1answer
40 views
Fastest way to ArrayFlatten a 2D array of 2D arrays, both for Sparse and Dense
I am using Mathematica 12 and want to know what is the fastest way to transform a 2D array of 2D arrays both for dense and sparse arrays. I remember looking for this a few versions of Mathematica ago, ...
4
votes
1answer
78 views
How to speed up this SparseArray construction
This code is (obviously) getting slower with the growing number of trials, currently running over 5 hours. This stylised example takes 2.5 minutes. It is not entirel illustrative as the real situation ...
1
vote
0answers
62 views
6
votes
1answer
45 views
NearestTo causes a kernel crash when applied to a list of SparseArrays [closed]
Nearest and NearestTo cause a kernel crash on Mathematica 12.0.0 for Mac OS X. (running on OS X 10.11.6) when operating on a list of SparseArray vectors.
Here's my minimal breaking example:
...
0
votes
1answer
68 views
How does Indexed work in terms of sparse array
I want to use indexed given that s is an element [0,500] but I am unsure how to write that without getting a format error or a tensor error.
...
0
votes
0answers
96 views
Determining the price of an option using Black-Scholes
Code for randomly generated interest rates:
...
3
votes
1answer
29 views
Condition in SparseArray does not check the condition for some matrix elements
Consider the following MWE:
SparseArray[{{i_, j_} /; (IntegerDigits[i - 1, 2, 2][[1]] == 0) :> 1}, {4, 4}]
This should give a $4\times 4$ matrix in which the ...
2
votes
1answer
41 views
How can I create SparseArray by imposing conditions?
I have two lists: one for directed links list1 and another list2 for the values associated with the links.
...
7
votes
2answers
215 views
Fastest way to update rows of an array of SparseArrays
I have an array of sparse arrays (check update 3 below for a concrete example that has the same qualitative features as what I use in my real code) , say
...
0
votes
0answers
24 views
Filling Regions (Blocks) of a Binary Matrix with Different Probabilities
This is an extension of the following question:
How to generate binary array whose elements with values 1 are randomly drawn, where the most elegant answer was posted in the comments:
...
4
votes
1answer
104 views
Efficiently calculating matrix exponential of a recursively generated matrix
Given a matrix $A$ of size $N \times N$, I want to evaluate the function
\begin{equation}
F(t) = |Tr(\exp^{-i A t})|^2
\end{equation}
as a function of $t$. Here, $A[n]$ is constructed recursively ...
2
votes
1answer
44 views
Efficient Linear Operators on SparseArrays
I have a rank four SparseArray of dimension {40, 40, 40, 40}. I wish to apply a linear operator to it, whose form I know abstractly. That is, I have a simple closed form for the action of the operator ...
2
votes
1answer
77 views
How to RowReduce a sparse matrix?
I want to compute the reduced row echelon form of a sparse matrix, but RowReduce returns a dense matrix. Is there a build-in function that computes the reduced form ...
4
votes
3answers
105 views
Sparse matrix processing: flip sign of top-left entries of the matrix
I have a 12k X 12k sparse array (~1% density) and I need to:
take the square root of all the elements
flip the sign of all the elements in the top-left half of the matrix
For example, say that the ...
7
votes
1answer
173 views
Finding the null space of a large sparse matrix
I am trying to compute the null space of a large $n\times n$ sparse matrix. No matter how large the dimension of the matrix is, it will always look like as below:
The figure on the left shows the ...
4
votes
0answers
65 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 ...
3
votes
1answer
68 views
Signed cell adjacency matrices (boundary operators)
In How to obtain the cell-adjacency graph of a mesh? there are some great answers that show how to obtain the cell adjacency matrix of a mesh. How would one generalize these to incorporate the ...
18
votes
1answer
389 views
Efficiently defining a SparseArray function
I've got a fairly large SparseMatrix (~60,000 entries in a ~10,000-by-10,000 matrix) that depends on two parameters (im1 and <...
6
votes
1answer
146 views
Speeding up tensor contractions and multiplication
Consider a tensor $T\in\mathbb{R}^{N\times N\times N\times M}$ and two vectors $x,y\in\mathbb{R}^N$. I want to compute the $N\times M$ vector defined by $X_{ij}=\operatorname{tr}(x^\top T_{:,:,i,j}y)=\...
1
vote
0answers
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 ...
asked Jun 27 '19 at 22:48
AccidentalFourierTransform
8,5331 gold badge14 silver badges48 bronze badges
8
votes
1answer
85 views
SparseArray: how to efficiently extract/delete many entries?
This is a follow-up of this question. We have a large $m\!\times\!n$ matrix stored as a SparseArray a and a list of positions pos...
18
votes
3answers
380 views
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)
$$y''(x)=\sin(x),\ y(0)=0,\ y(...
10
votes
3answers
540 views
Optimising subdiagonal shift matrix generation time
I want a square matrix $A$ such that $$A_{i,i-1} = 1 \ \forall i\\ A_{i,j} = 0 \text{ for } \ j \ne i-1$$
I have tried
...
5
votes
2answers
229 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
36 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
59 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
571 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 ...
14
votes
2answers
996 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 ...
10
votes
2answers
715 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
962 views
9
votes
0answers
142 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 ...
2
votes
1answer
230 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
124 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
78 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
190 views
Delete zeros from a sparse array [duplicate]
Why doesn't SparseArray automatically remove zero entries? The code
...
1
vote
2answers
64 views
1
vote
1answer
24 views
4
votes
3answers
294 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 ...
33
votes
1answer
2k views
Complex eigenvalues from a sparse Hermitian matrix
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
70 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
239 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
65 views
1
vote
1answer
49 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
34 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
53 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
193 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
107 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
175 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
...
