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

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3
votes
0answers
87 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, ...
3
votes
1answer
116 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 ...
4
votes
2answers
218 views

Upsampling matrix by inserting zeros inbetween 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 ...
9
votes
2answers
217 views

Additive SparseArray Assembly

The goal is to assemble a SparseArray in an additive fashion. Let us assume we have a large List of indices (some will be ...
1
vote
3answers
109 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: ...
2
votes
1answer
211 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 $1$, ...
4
votes
3answers
407 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
votes
0answers
97 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) ...
4
votes
1answer
136 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
votes
1answer
249 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 ...
5
votes
1answer
97 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 ...
1
vote
0answers
43 views

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

Build a 100.000.000 by 10 element SparsArray. Fill position 1/1 and 100.000.000/10 with a value 999.999.999.999.999. ...
2
votes
1answer
213 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
333 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 ...
2
votes
3answers
421 views

Dynamically filling matrix with a[[n,m]] = 1/a[[m,n]]

I'm building a square matrix, with 1s on the diagonal and elements in U the inverse of elements in L, which are random integers drawn from the sequence 1, ..., 9. Given the nature of the problem I ...
6
votes
0answers
180 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
votes
6answers
714 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
188 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
votes
1answer
512 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 ...
9
votes
2answers
366 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 ...
5
votes
1answer
215 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 $A^{mn}$ ...
1
vote
1answer
754 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 ...
6
votes
1answer
326 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 ...
15
votes
1answer
344 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. ...
5
votes
2answers
356 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
votes
1answer
2k 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
221 views

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

Here is my code: ...
10
votes
1answer
735 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: ...
9
votes
2answers
488 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 ...
10
votes
2answers
561 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
3
votes
1answer
256 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 ...
8
votes
1answer
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 ...
3
votes
3answers
400 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?
22
votes
2answers
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 ...
8
votes
2answers
723 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 ...
16
votes
3answers
976 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 ...