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

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30
votes
1answer
635 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: ...
23
votes
2answers
1k 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 MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
19
votes
3answers
1k 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 ...
19
votes
1answer
221 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 ...
18
votes
2answers
217 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 ...
18
votes
1answer
494 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
votes
1answer
380 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'...
17
votes
1answer
313 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 and fixed in 10.3.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 ...
16
votes
1answer
725 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
votes
6answers
829 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 &...
15
votes
2answers
251 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: ...
15
votes
1answer
280 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: ...
14
votes
2answers
2k 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 ...
13
votes
2answers
637 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 ...
12
votes
2answers
302 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 ...
11
votes
2answers
692 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
11
votes
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 ...
11
votes
0answers
265 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" ...
10
votes
2answers
495 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 ...
10
votes
2answers
253 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
10
votes
2answers
445 views

Speed up 4D matrix/array generation

I have to fill a 4D array, whose entries are $\mathrm{sinc}\left[j(a-b)^2+j(c-d)^2-\phi\right]$ for a fixed value of $\phi$ (normally -15) and a fixed value of $j$ (normally about 0.00005). The way I'...
10
votes
1answer
205 views

Sporadic bugs in multidimensional SparseArray objects

Udate This SparseArray[] bug is (apparently) fixed on version 10.0 ...
10
votes
1answer
150 views

Something wrong when I apply Derivative on a SparseArray

Bug introduced in v5.0 or earlier, and persisting through v10.4.1. There, I create a SparseArray using command ...
10
votes
2answers
121 views

Using Cases to pick out entries of a SparseArray

I'm trying to use a SparseArray for some large homological algebra calculations. I'd like to find indices of a SparseArray ...
10
votes
1answer
968 views

Sparse convolution of sparse arrays

The documentation for ListConvolve mentions that "ListConvolve works with sparse arrays", which is true. The result, however is never sparse, eg: ...
10
votes
0answers
118 views

Possible Bug in LinearSolveFunction with Sparse Vectors

Bug introduced in 5.0 and persists through 10.4.1 LinearSolveFunction is new in 5.0 Consider the following set of equations and corresponding variables: ...
10
votes
0answers
123 views

Efficient solution of huge sparse linear system

I'm trying to improve efficiency of my code in which main task is a solution to huge (~$10^4\times 10^4$) but sparse linear system $$Ax=b$$ (In fact my aim is to solve nonlinear equations $F(x)=0$, ...
9
votes
4answers
266 views

How to convert a sparse matrix to a list of sparse arrays?

I have a matrix stored as a SparseArray. How can I convert it to a List of its rows, where each row is stored as a ...
9
votes
2answers
290 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 ...
9
votes
2answers
176 views

Does LinearSolve know that I gave it a Sparse lower triangular matrix?

Let $\mathbf L$ be a nonsingular numeric (non-symbolic) large, lower triangular sparse matrix. Let $\mathbf b$ be an appropriately sized vector. I want to solve $\mathbf L\mathbf x=\mathbf b$. ...
9
votes
1answer
1k 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 ...
9
votes
0answers
158 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: ...
8
votes
2answers
307 views

Why is IdentityMatrix not defined as a SparseArray by default?

Simple (possibly silly) question: why are IdentityMatrix, DiagonalMatrix, ConstantArray ...
8
votes
2answers
947 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 ...
8
votes
1answer
111 views

SparseArray output triggers “unsafe dynamic content” warning

The first basic example in the documentation of SparseArray: ...
8
votes
1answer
244 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. <...
7
votes
3answers
163 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 ...
7
votes
1answer
174 views

Instant kernel crash when using `+=` on `SparseArray` with repeated entries

Bug introduced in 5.2 and fixed in 10.1.0 Not sure if this is known behavior or not, but the following two lines produce an instant kernel crash (I'm using Mathematica 10.0.1 Windows 64-bit): <...
7
votes
1answer
156 views

Possible bug: SparseArray Part assignment loses default value?

fixed in 10.0.2 This sure looks like a bug to me (Mathematica 10.0.0, MacOS): ...
7
votes
1answer
405 views

How to produce the ILU0 or ILUT as stand-alone procedures on sparse matrices?

Mathematica uses the ILU0 procedures automatically to precondition large sparse linear systems; e.g. ...
6
votes
1answer
118 views

Adding two SparseArrays produces zeros in the reported “NonzeroValues”

When two SparseArrays are added together and new zero values are created, these new zero values are reported as "NonzeroValues". Example, produced with Mathematica version 10.2: ...
6
votes
1answer
409 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 ...
6
votes
0answers
185 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 <...
5
votes
3answers
427 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
votes
4answers
536 views

Elegant mehod of generating this matrix?

Good evening, I need to determine an elegant (as possible) method of computing an nxn matrix below (the matrix shown is just a 16x16 example). I've been toying with For loops, Tables, Bands, ...
5
votes
4answers
160 views

Add to matrix missing elements (for list of time series)

This question is an extension of the 43122. I’ve looked through many interesting post (like this) but (as always) missed the direct matching. So the setting is simple: ...
5
votes
1answer
212 views

How can I efficiently ArrayFlatten a matrix of sparse matrices?

I have a matrix of sparse matrices that I want to convert to a sparse block matrix. So, basically I want what ArrayFlatten does, except that I want the output to be ...
5
votes
3answers
188 views

How to populate a large sparse array efficiently

I am trying to populate a large 2D sparse array and sum up all the columns at the end. I tried generating a set of rules and then generate a matrix using SparseArray or break the data into chunks but ...
5
votes
1answer
237 views

What's wrong with this code to create a matrix?

Here is my code: ...