# Tagged Questions

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

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### 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 ...
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 ...
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 ...
692 views

### Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
641 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: ...
949 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 ...
290 views

The goal is to assemble a SparseArray in an additive fashion. Let us assume we have a large List of indices (some will be ...
111 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 100....
562 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 (...
914 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 ...
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 ...
381 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'...
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: ...
111 views

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

The first basic example in the documentation of SparseArray: ...
684 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 ...
282 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: ...
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: ...
403 views

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

s = Import["hello.mat"]; t = GraphEmbedding[Graph[s[[1]]], "GridEmbedding"]; I get the following error: GraphEmbedding::graph: A graph object is expected ...
606 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 ...
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 ...
727 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 ...
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 ...
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 ...
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 ...
298 views

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### Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
267 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" ...
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 ...
429 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 & ... &...
138 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 ...
194 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 ...
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): <...
118 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 ...
237 views

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

Here is my code: ...
65 views

### How to create overlapped block matrices and simplify the result

This is sort of a duplicate of Creating overlapped block matrices, but the question wasn't fully answered since the OP never returned to clarify. I am using Kuba's answer for FEM, but I have been ...
487 views

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

I have a band matrix ...
821 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 ...
134 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 ...
472 views

### Support for Compressed Sparse Column sparse matrix representation

Is there native support for Compressed Sparse Column (CSC) format for sparse matrices, like importing and manipulating them?