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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136 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 ...
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1answer
61 views

Interactively Manipulate SparseArrays or Lists

I'd love to use SparseArrayor List to group a set of parameters together in a function. ...
7
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1answer
178 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): ...
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0answers
197 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: ...
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2answers
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. <...
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1answer
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: ...
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2answers
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 ...
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0answers
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.
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1answer
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 ...
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1answer
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 ...
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1answer
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: ...
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1answer
390 views

How to handle a sparse array of lists

I have data in the form of a sparse array of lists. For example: ...
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0answers
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 ...
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2answers
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: ...
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2answers
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 ...
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2answers
639 views

Manipulating sparse array elements

Suppose I have two sparse arrays ...
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3answers
5k 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 ...
4
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3answers
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 ...
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0answers
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 ...
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1answer
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 ...
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1answer
200 views

Product of non-zero elements in sparse array

How can I multiply the non-zero elements of a SparseArray? Example: ...
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1answer
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: ...
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0answers
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, ...
7
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1answer
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 ...
7
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3answers
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 ...
5
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2answers
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 ...
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2answers
545 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 ...
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3answers
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: ...
4
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1answer
439 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 $1$, $...
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3answers
1k 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 (...
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0answers
114 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
191 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 ...
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1answer
1k 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
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1answer
191 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 $100000000 \times 10$ ...
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0answers
53 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
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1answer
464 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 ...
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1answer
771 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 ...
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1answer
333 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
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1answer
304 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 ...
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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
370 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
720 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
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1answer
355 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
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3answers
986 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
451 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
987 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
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1answer
268 views

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

Here is my code: ...