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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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52
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2answers
2k views

What are SparseArray Properties? How and when should they be used?

A strange undocumented form of SparseArray is increasingly used in answers on this site: ...
14
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2answers
899 views

How to interpret the FullForm of a SparseArray?

SparseArrays are atomic objects, but they do have a FullForm which reveals information about them. What is the meaning of the ...
21
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3answers
5k 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 ...
15
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2answers
516 views

Additive SparseArray Assembly

The goal is to assemble a SparseArray in an additive fashion. Let us assume we have a large List of indices (some will be ...
20
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3answers
2k views

Efficient way to combine SparseArray objects?

I have several SparseArray objects, say sa11, sa12, sa21, sa22, which I would like to combine into the equivalent of {{sa11, sa12}, {sa21, sa22}}. As an example, I ...
10
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2answers
1k views

Efficient by-element updates to SparseArrays

I have a very large SparseArray called A. What is the most efficient way to update say element ...
11
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2answers
805 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
7
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1answer
188 views

How to relate memory usage with occupied positions of SparseArrays?

What is the relation of memory usage of a SparseArray and the number of its occupied positions? Let's say you build a $100000000 \times 10$ ...
23
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2answers
827 views

Speeding up generation of block diagonal matrix

I'm struggling with the following problem. I have $48$ square matrices (full, filled with real machine precision numbers, thus are packed, all different) of size $128$. I wolud like to place them on a ...
19
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1answer
654 views

Why won't SparseArray let me store values with the head List?

When you attempt to define a SparseArray with elements that have the head List it complains: ...
2
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1answer
1k views

Import Excel sheet into 3D array?

I have an excel spreadsheet that I would like to plot in a 3D graph using mathematica. The X and Y values are the location of the cell, and the Z value is the number of the scale. How can I import ...
50
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2answers
2k 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 ...
18
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3answers
1k views

Using ReplaceAll on SparseArray

I'm using SparseArray in a notebook in which I am doing complex conjugation manually, i.e. writing $\sqrt{-1}$ as i and applying ...
5
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3answers
1k views

SparseArray row operations

Given a large (very) sparse matrix, A, how can I efficiently "operate" on only the nonzeros in a given row? For example: For each row in A, generate a list of column indices that have a magnitude (...
10
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1answer
202 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 ...
6
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2answers
227 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 ...
17
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1answer
444 views

Adding three integer sparse matrices is very slow. Adding only two is fast

Bug introduced in 9.0.0 and fixed in 10.0.0 Adding more than two sparse matrices in one step in Mathematica 9 is very slow (in fact I couldn't even wait for it to finish). Here's an example. Let's ...
26
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2answers
2k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in Mathematica (which I found through this SO answer): essentially, I want to differentiate noisy data. ...
15
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2answers
266 views

Bug with SparseArray selector in Pick

Bug introduced in version 8 or earlier and fixed in 10.0 I have created a notebook with two cells. This is the content of the first: ...
11
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2answers
435 views

Building sparse array from packed arrays

Suppose I have two large packed arrays a and b, that respectively contain the position of the elements of a square matrix (i.e. <...
10
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1answer
171 views

SparseArray output triggers “unsafe dynamic content” warning

The first basic example in the documentation of SparseArray: ...
20
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0answers
868 views

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" ...
17
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2answers
240 views
6
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1answer
67 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"] ...
3
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1answer
1k views

How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
2
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1answer
1k views

How to find position of non-zero elements in SparseArray without converting to a dense object

Overview So I have a SparseArray, sparse, constructed from a list of rules, with the dimension options. Given a row, I want to know where the values are non-zero. ...
2
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2answers
1k views

Create a matrix of matrices using Band and ArrayFlatten [duplicate]

I can easily write a simple Band matrix using: SparseArray[{Band[{2, 1}] -> a}, {Dim, Dim}] where a is a number. Now, I ...
0
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0answers
95 views

Determining the price of an option using Black-Scholes

Code for randomly generated interest rates: ...
17
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1answer
1k views

How to use SparseArray in CUDA?

Sparse arrays are widely used in many scientific applications where memory and time are strictly limited. For a considerable speedup one can use CUDA. Since Mathematica 8 we can conveniently use CUDA ...
15
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2answers
420 views

Temporal database reconstruction in mathematica

<EDIT> after some internet research I found the database domain that deals with this kind of thing: Temporal Databases. I think my question therefore becomes how to reconstruct a temporal ...
20
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1answer
336 views

What are pattern sparse arrays and how do I use them?

I found a few references to something called a "pattern sparse array" that does not contain any values, only positions. What is this data structure? How and when do I use it? From the documentation ...
14
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2answers
986 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 ...
6
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2answers
2k views

How to export an output matrix obtained in mathematica to a matrix in python with the correct format?

I have a large sparse matrix as the output and I want to save the output and open it as a matrix in python. The output is a 6000 x 6000 matrix and I don't know how to make changes to the file such ...
11
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1answer
3k views

How to work around Mathematica hanging when showing a large SparseArray?

Bug introduced in 9.0 and fixed in 9.0.1 In Mathematica 9, if I display any large SparseArray object in the default way (which looks something like ...
5
votes
4answers
590 views

Constructing a large tridiagonal matrix with alternating signs

What is the best way to construct a large tridiagonal matrix, in the following form (notably with alternating signs)? $\mathbf M = \begin{pmatrix} 0 & a & 0 & 0 & 0 & \cdots \...
11
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3answers
339 views

Most efficient way to build block / banded SparseArray

I have a matrix that I generate with a procedure that looks like this: ...
15
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6answers
1k views

Matrix Rotation

If I have a matrix of any size, say $\begin{pmatrix} 72 & 32 & 64 \\ 18 & 8 & 16 \\ 63 & 28 & 56 \\ \end{pmatrix}$ $\begin{pmatrix} 72 & 32 \\ 18 & 8 \\ 63 &...
11
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2answers
643 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
9
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1answer
297 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 <...
6
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1answer
113 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. ...
19
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1answer
1k views

Sparse Cholesky Decomposition

I am working with square matrices with a special form, which for large rank ($> 100,000$) would be best stored and manipulated as a SparseArray. I believe that ...
17
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0answers
462 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 ...
9
votes
1answer
2k views

Exporting a Large Multidimensional Sparse Array

I'm trying to export a sparse array from Mathematica to share with collaborators who primarily use Matlab. The sparse array in question is 4 dimensional, (72 x 93 x 94 x 172) with ~4M non-zero ...
7
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0answers
77 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 ...
7
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3answers
918 views

How to create a large sparse block matrix

I need to generate a very large sparse block matrix, with blocks consisting only of ones along the diagonal. I have tried several ways of doing this, but I seem to always run out of memory. The ...
7
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1answer
243 views

Opposite function to Normal

Is there any function opposite to Normal? For example, let as say that I have an SparseMatrix A, then, let as say that for convenience for a certain operation like Packing, I convert it into an Array ...
7
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2answers
206 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 ...
5
votes
3answers
3k views

Constructing Tri-Diagonal Matrices

Fractional Calculus Course, we are instructed to create an $n \times n$ Tri-Diagonal matrix in the form of: \begin{array} a A &= \begin{bmatrix} 2 & -1 & 0 & 0 & ... &...
5
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1answer
191 views

Assigning Sequence to Part of a SparseArray (bug?)

Part ▪ You can make an assignment like t[[spec]]=value to modify any part or sequence of parts in an expression. ▪ If <...
4
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3answers
1k views

Finding elements from a sparse matrix

I am dealing sparse matrices of very large dimensions. I need to locate the positive and negative elements of the matrices and make lists of their corresponding positions. Of course I can write a ...