# 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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### 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: ...
454 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. <...
169 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 ...
463 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.
71 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 ...
555 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 ...
650 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: ...
388 views

### How to handle a sparse array of lists

I have data in the form of a sparse array of lists. For example: ...
133 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 ...
271 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: ...
156 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 ...
637 views

### Manipulating sparse array elements

Suppose I have two sparse arrays ...
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### 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 ...
66 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 ...
244 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 ...
200 views

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

How can I multiply the non-zero elements of a SparseArray? Example: ...
455 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: ...
178 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, ...
256 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 ...
818 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 ...
529 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 ...
542 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 ...
146 views

### ArrayRules for a ragged list

Let there be a sample list as , l = {a, {{b, c}}, {d, e}, {f}, {{g, {y}, u, h}, {{{{k, j}}}}},k, {{{{q}, {w}, {r}, {x}}}}}; ArrayRules[l] ArrayRules::rect: ...
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### Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...