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

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2
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1answer
108 views

When are sparse arrays effective?

Sparse arrays are not effective in Mathematica 10. More computational time is needed to perform arithmetic operations on sparse arrays. Their size is also bigger than normal arrays. Here is a simple ...
8
votes
2answers
181 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
2
votes
0answers
41 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
4
votes
0answers
66 views

How can I force the use of sparse diagonalization methods?

When I evaluate the Eigenvalues function on a very large (e.g. 2^16 x 2^16) sparse matrix, Mathematica says something like: Because finding 65536 out of the ...
2
votes
1answer
51 views

Non-numeric elements in banded sparse array

The documentation mentions that "the elements in SparseArray need not be numeric", although "the individual elements of a sparse array cannot themselves be lists." ...
15
votes
0answers
201 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 array with symbolic ...
2
votes
4answers
167 views

Given a matrix of integer, create a matrix with 1 or 0 according to which numbers are in the first matrix

Not sure the title gives the idea of what I need, so here is a sample: I have ten (w) combinations (subsets) of 20 (n) numbers taken 4 (k) at time. I need a matrix of dimension w x n with 0/1 in each ...
2
votes
1answer
96 views

Memory usage optimization for a large Association/SparseArray

Reformulating my question in simpler terms. Take two lists list1 = RandomInteger[{1, 100000000}, 25000000]; list2 = RandomReal[{1, 10}, 25000000]; Make an ...
18
votes
1answer
399 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: ...
2
votes
0answers
71 views

Memory used by SparseArray objects

In dealing with a quantum mechanics problem, I am representing some many-body states in two different ways in Mathematica. For two parameters n and ...
1
vote
2answers
67 views

conditional rules for sparse matrix

why does the following not work (Table isn't plugging in values for k): ...
-1
votes
1answer
100 views

Laplace equation

I tried to run this code, but it doesn't work for NDSolve ...
-2
votes
1answer
91 views

Recreating in Mathematica a matrix created in Python [closed]

I need to recreate in Mathematica this matrix that I created in Python: ...
1
vote
2answers
100 views

Filing matrix by bands [closed]

I need to fill a matrix, CSI, by taking elements from an array, inverse, which is the Inverse Fast Fourier Transform of an array ...
2
votes
1answer
72 views

sparse array with list [closed]

i'm trying to populate a sparse array with lists in certain positions, i tried the following code, ...
3
votes
1answer
97 views

speeding up creation of SparseArray

I have to create the following sparse arrays, which are reshaped in a two dimensional matrix, so that i can use the build in Dot[] function to do a kind of ...
5
votes
4answers
519 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, ...
4
votes
0answers
40 views

Bug? Kernel Crash on SparseArray access [duplicate]

Bug introduced in 5.2 and fixed in 10.1.0 The following simple code s = SparseArray[{}, {10, 10}] s[[1, {1, 2, 3, 1, 1}]] = {a, b, c, d, e} on my machine ...
4
votes
1answer
59 views

SparseArray output triggers “unsafe dynamic content” warning

The first basic example in the documentation of SparseArray: ...
7
votes
1answer
157 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): ...
1
vote
1answer
77 views

Entering block matrices, general case doesn't work

I want to enter several matrices at different positions in blocks. There is already a very similar answer here: http://mathematica.stackexchange.com/a/3562/6138 I thought that simply generalizing ...
0
votes
0answers
42 views

Permute indices of a large sparse array

I'm starting with a very large rank 3 tensor, F, that is stored as a SparseArray, and I need to permute its indices. I first tried using ArrayRules to get the positions of the non-zero elements, to ...
2
votes
2answers
67 views

editing entries of a sparse array + sparse Smith normal form

Why does the following code ...
11
votes
2answers
239 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 ...
13
votes
1answer
385 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 ...
3
votes
1answer
299 views
14
votes
1answer
215 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: ...
4
votes
1answer
178 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
4
votes
1answer
110 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
150 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 ...
1
vote
1answer
71 views

Conditions in SparseArray

I got confused by {i_, j_} /; in the following code. I didn't see an explanation in the SparseArray documentation. Can anyone ...
0
votes
1answer
38 views

Interactively Manipulate SparseArrays or Lists

I'd love to use SparseArrayor List to group a set of parameters together in a function. ...
7
votes
1answer
135 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): ...
8
votes
1answer
191 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. ...
1
vote
1answer
69 views

Devising a sparse array rule

Suppose I have a matrix A={{1, 2}, {3, 4}} that defines the positions of non-zero values in a sparse array: ...
2
votes
2answers
344 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
votes
1answer
56 views

What's wrong with my rule? [duplicate]

Consider a simple code to form a SparseArray: Q = 5; a = Table[i, {i, Q}]; SparseArray[{{j_} /; j > 2 -> a[[j]]}, {Q}] Part::pspec: Part specification j ...
3
votes
1answer
367 views

Transforming a huge rectangular table to Sparse Array

I am interested in the most efficient way to transform a huge rectangular array to a sparse array structure. Consider a numeric rectangular table that is rather sparse, with zero positions being set ...
3
votes
1answer
242 views

Are there any more time-efficient ways to solve a matrix equation than with SparseArray and LinearSolve?

I am trying to solve a matrix equation, with the matrix being tridiagonal. The problem I am having is that a message keeps appearing that I don't have enough memory. Here is the code: ...
2
votes
1answer
158 views

How to handle a sparse array of lists

I have data in the form of a sparse array of lists. For example: ...
5
votes
0answers
105 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 ...
12
votes
2answers
211 views

Bug with SparseArray selector in Pick

I have created a notebook with two cells. This is the content of the first: ...
4
votes
2answers
131 views

Values (or positions) of array row elements within a specified number of positions from target value

I have the need to collect values from the rows of rectangular arrays of arbitrary precision integers, given a target element value and allowed "distance" (positions +/- within the row from found ...
1
vote
2answers
229 views

Manipulating sparse array elements

Suppose I have two sparse arrays ...
12
votes
2answers
949 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 ...
4
votes
3answers
611 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 ...
0
votes
0answers
71 views

Is there a faster way to do Normal[SparseArray[{{1,1,1}→1.2, {1,1,2}→20.2, …, {m,n,p}→0.3}]]?

I have a list of the form {{1,1,1}→1.2, {1,1,2}→20.2, ..., {m,n,p}→0.3} and I want to create an $m \times n \times p$ array, $A$, where the value of $A[[i,j,k]]$ is ...
1
vote
0answers
51 views

Addition of sparse array objects [duplicate]

Bug introduced in 9.0.0 and fixed in 10.0.0 I have been having some trouble with the addition of large (but very sparse) matrices using SparseArray. Here is the simplest example to illustrate the ...
10
votes
1answer
196 views

Sporadic bugs in multidimensional SparseArray objects

Udate This SparseArray[] bug is (apparently) fixed on version 10.0 ...
2
votes
1answer
141 views

Product of non-zero elements in sparse array

How can I multiply the non-zero elements of a SparseArray? Example: ...