# 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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### 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" ...
193 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 ...
154 views

### conditional rules for sparse matrix

why does the following not work (Table isn't plugging in values for k): ...
243 views

### Laplace equation

I tried to run this code, but it doesn't work for NDSolve ...
145 views

### Recreating in Mathematica a matrix created in Python [closed]

I need to recreate in Mathematica this matrix that I created in Python: ...
135 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 ...
334 views

### sparse array with list [closed]

i'm trying to populate a sparse array with lists in certain positions, i tried the following code, ...
196 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 ...
633 views

### Elegant method of generating this matrix?

Good evening, I need to determine an elegant (as possible) method of computing an $n\times n$ matrix below (the matrix shown is just a $16\times16$ example). I've been toying with ...
47 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 (...
167 views

### SparseArray output triggers “unsafe dynamic content” warning

The first basic example in the documentation of SparseArray: ...
203 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): ...
125 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: https://mathematica.stackexchange.com/a/3562/6138 I thought that simply generalizing ...
131 views

### editing entries of a sparse array + sparse Smith normal form

Why does the following code ...
414 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 ...
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 ...
920 views

### How to speed up band matrix-matrix multiplication?

I have a band matrix ...
644 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: ...
429 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 \\ & &{} + \int_{x_0}...
253 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 ...
913 views

### How to convert a sparse array to a graph?

s = Import["hello.mat"]; t = GraphEmbedding[Graph[s[]], "GridEmbedding"]; I get the following error: GraphEmbedding::graph: A graph object is expected ...
402 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 ...
125 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 ...
59 views

### Interactively Manipulate SparseArrays or Lists

I'd love to use SparseArrayor List to group a set of parameters together in a function. ...
177 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): ...
193 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: ...
427 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. <...
154 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: ...
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 ...
430 views

### The Jacobi-Davidson method

Does any implementation of the Jacobi-Davidson method for Mathematica exist? A highly parallelized version for sparse matrices would be of special interest.
68 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 ...
522 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 ...
634 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: ...
334 views

### How to handle a sparse array of lists

I have data in the form of a sparse array of lists. For example: ...
132 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 ...
261 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: ...
153 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 ...
581 views

### Manipulating sparse array elements

Suppose I have two sparse arrays ...
4k 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 ...
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 ...
64 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 ...
240 views

### Sporadic bugs in multidimensional SparseArray objects

Bug introduced in 9.0 and fixed in 10.0 Update This SparseArray[] bug is (apparently) fixed on version 10.0 ...
195 views

### Product of non-zero elements in sparse array

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

### Specify positions in a SparseArray using patterns with functions

I spent some time trying to figure out what was what was making so slow the calculation of the following array(actually this is only a SUPERsimple toy model): Input to the array: ...
170 views

### Efficient storage of Kronecker sum of circulant matrices+diagonal matrix

I have a square matrix of the form $$M=D+\overset{N}{\underset{n=1}\bigoplus}R_n,$$ where $R_n$ are circulant matrices, $D$ is a diagonal matrix and $\oplus$ is Kronecker sum. Its size is quite big, ...
238 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 ...
762 views

### Approximate minimum degree permutation algorithm in Mathematica

In MATLAB there is a nice implementation of the so called AMD (approximate minimum degree permutation) algorithm named amd (see Online MATLAB Documentation). There is an alternative algorithm called ...
449 views

### Upsampling matrix by inserting zeros in between 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 ...