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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3
votes
1answer
431 views

How to create a SparseArray satisfying multiple conditions on Parts and Elements of a Matrix?

I have a matrix m1 of size $3 \times 19$. Rows $1$, $2$ and $3$ represent $3$ different groups, and columns represent $4$ different blocks: block1 - columns $1$, $...
5
votes
3answers
983 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 (...
3
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0answers
110 views

Det and MatrixRank freezes on SparseArray with nonzero default value

Bug introduced in 7.0 or earlier and fixed in 9.0.1 or earlier Why does the following simple code never come to an end (at least with version 8) ...
5
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1answer
189 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 <...
0
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1answer
885 views

Is it in general faster to get the eigenvectors and eigenvalues of a dense array rather than a sparse array?

I always thought that things in general go faster when working with sparse array but, I got this: Eigenvalues::arhm: Because finding 144 out of the 144 ...
7
votes
1answer
187 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 $100000000 \times 10$ ...
1
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0answers
52 views

How to estimate system resource usage of a SparseArray? [duplicate]

Build a 100.000.000 by 10 element SparseArray. Fill position 1/1 and 100.000.000/10 with a value 999.999.999.999.999. ...
2
votes
1answer
441 views

How to combine SparseArray and If

Because I am dealing with huge matrixes, my computer can not handle it, because of the memory. But, in my matrix, a very small percentage of the elements are non-zero. So I should use SparseArray as ...
1
vote
1answer
703 views

How to store a SparseArray? [duplicate]

How to Export/Write a SparseArray? How to Import/Read a SparseArray? Is it always stored as a normal array? How can it be stored in a dense form? Is a numerical SparseArray different to Export/Import ...
9
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1answer
269 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 <...
15
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6answers
1k 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 &...
5
votes
1answer
287 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 ...
3
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1answer
1k 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 ...
4
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1answer
325 views

How to accelerate updating some parts of sparse matrices?

I am trying to update some parts of an specific matrix as rapidly as possible. In what follows, I first set up the basics things that I want to use ...
10
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2answers
665 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 I'...
5
votes
1answer
311 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 $A^{mn}$ ...
2
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1answer
1k 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 ...
7
votes
3answers
876 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 ...
17
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1answer
441 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's ...
14
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2answers
817 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 ...
11
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1answer
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 ...
5
votes
1answer
265 views

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

Here is my code: ...
10
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1answer
2k 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: ...
18
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3answers
1k 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 ...
11
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2answers
797 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
3
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1answer
453 views

Efficiently importing XPM matrix data into Mathematica

The XPM file format is an image file format. Although it is primarily intended for icon pixmaps, it can also be used to store matrix data. For example, the GROMACS chemical simulation package uses ...
9
votes
1answer
2k 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 ...
8
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1answer
600 views

How to produce the ILU0 or ILUT as stand-alone procedures on sparse matrices?

Mathematica uses the ILU0 procedures automatically to precondition large sparse linear systems; e.g. ...
4
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3answers
621 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?
26
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2answers
2k 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 Mathematica (which I found through this SO answer): essentially, I want to differentiate noisy data. ...
10
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2answers
1k 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 ...
20
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3answers
2k 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 ...