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

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25
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1answer
484 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: ...
22
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
1answer
159 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
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 ...
18
votes
1answer
411 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
2answers
182 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 ...
17
votes
1answer
294 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
365 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. ...
15
votes
6answers
768 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
1answer
531 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
2answers
237 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
242 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: ...
12
votes
2answers
554 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
1k 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 ...
12
votes
2answers
278 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
638 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
11
votes
1answer
2k 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 ...
10
votes
2answers
224 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
10
votes
2answers
413 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 ...
10
votes
1answer
201 views

Sporadic bugs in multidimensional SparseArray objects

Udate This SparseArray[] bug is (apparently) fixed on version 10.0 ...
10
votes
1answer
841 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: ...
9
votes
2answers
450 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 ...
9
votes
2answers
260 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
159 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
83 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 $F(x)=0$, ...
8
votes
2answers
824 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
104 views

SparseArray output triggers “unsafe dynamic content” warning

The first basic example in the documentation of SparseArray: ...
8
votes
1answer
216 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
1answer
164 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
145 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): ...
6
votes
1answer
98 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
368 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
183 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
4answers
524 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
173 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
4answers
133 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
173 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
1answer
230 views

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

Here is my code: ...
5
votes
1answer
104 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 100.000.000 by 10 element SparseArray. And fill the two position 1/1 and ...
5
votes
1answer
202 views

Why is Flattening a CoefficientArray so slow?

I have a vector of $n$ degree $n$ polynomials in $(x,y,z)$, each of whose coefficients is an inhomogenous linear expression in $3 n^2$ variables. I want to write down the linear equations in these $3 ...
5
votes
1answer
232 views

Summing tensors in mathematica

How do I perform the following summation in mathematica? \begin{equation} \Sigma_{m=1}^5 e_{ijklm}A^{mn} \end{equation} I have the $e_{ijklm}$ tensor of rank 5 in 5 dimension as a array and $A^{mn}$ ...
5
votes
0answers
113 views

SparseArray internal structure [duplicate]

According to the documentation: SparseArray is treated as a raw object by functions like AtomQ and for purposes of pattern ...
4
votes
3answers
714 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 ...
4
votes
3answers
298 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 & ... ...
4
votes
3answers
472 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 ...
4
votes
2answers
245 views

Upsampling matrix by inserting zeros inbetween elements

I want to essentially take an image with $n \times n$ pixels and expand it into a sparse array, spacing out the pixels by a factor $2$ or $3$. Each pixel in the input image occupies one of the corners ...
4
votes
3answers
152 views

Problem with Conditionals: Why does mathematica add an extra empty list to my output

I have a set of positions where I want to slice a list of numbers. If I Total the values in that list, and they are greater than or equal to 1, I want to remember ...
4
votes
1answer
129 views

Parallelizing sparse array construction

I have a very large sparse array, and the computation of individual matrix elements is fairly expensive. The Matrix is Hermitian and traceless, so I would like to construct only the sub-diagonal ...
4
votes
1answer
147 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 ...