# Tagged Questions

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

1answer
40 views

### Entering block matrices, general case doesn't work

I want to enter several matrices at different positions in blocks. There is already a very similar answer here: http://mathematica.stackexchange.com/a/3562/6138 I thought that simply generalizing ...
0answers
15 views

### Permute indices of a large sparse array

I'm starting with a very large rank 3 tensor, F, that is stored as a SparseArray, and I need to permute its indices. I first tried using ArrayRules to get the positions of the non-zero elements, to ...
2answers
42 views

### editing entries of a sparse array + sparse Smith normal form

Why does the following code ...
2answers
158 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 ...
1answer
141 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 ...
1answer
163 views

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

I have a band matrix ...
1answer
125 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: ...
1answer
102 views

### Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
1answer
64 views

### Parallelizing sparse array construction

I have a very large sparse array, and the computation of individual matrix elements is fairly expensive. The Matrix is Hermitian and traceless, so I would like to construct only the sub-diagonal ...
1answer
96 views

### How can I efficiently ArrayFlatten a matrix of sparse matrices?

I have a matrix of sparse matrices that I want to convert to a sparse block matrix. So, basically I want what ArrayFlatten does, except that I want the output to be ...
1answer
55 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 ...
1answer
30 views

### Interactively Manipulate SparseArrays or Lists

I'd love to use SparseArrayor List to group a set of parameters together in a function. ...
0answers
78 views

### Possible bug: SparseArray Part assignment loses default value?

This sure looks like a bug to me (Mathematica 10.0.0, MacOS): ...
1answer
125 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. ...
1answer
54 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: ...
2answers
143 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 ...
1answer
48 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 ...
1answer
313 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 ...
1answer
169 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: ...
1answer
139 views

### How to handle a sparse array of lists

I have data in the form of a sparse array of lists. For example: ...
0answers
102 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 ...
2answers
199 views

### Bug with SparseArray selector in Pick

I have created a notebook with two cells. This is the content of the first: ...
2answers
120 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 ...
2answers
147 views

### Manipulating sparse array elements

Suppose I have two sparse arrays ...
3answers
488 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 ...
3answers
394 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 ...
0answers
61 views

### Is there a faster way to do Normal[SparseArray[{{1,1,1}→1.2, {1,1,2}→20.2, …, {m,n,p}→0.3}]]?

I have a list of the form {{1,1,1}→1.2, {1,1,2}→20.2, ..., {m,n,p}→0.3} and I want to create an $m \times n \times p$ array, $A$, where the value of $A[[i,j,k]]$ is ...
0answers
46 views

### Addition of sparse array objects [duplicate]

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 issue. First, I will define diagonal matrices ...
1answer
179 views

### Sporadic bugs in multidimensional SparseArray objects

Udate This SparseArray[] bug is (apparently) fixed on version 10.0 ...
1answer
112 views

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

How can I multiply the non-zero elements of a SparseArray? Example: ...
1answer
95 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: ...
0answers
70 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, ...
1answer
102 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 ...
2answers
173 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 ...
2answers
154 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 ...
3answers
103 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: ...
1answer
174 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 $1$, ...
1answer
143 views

### the way to save multidimensional array in text file [closed]

I have an array which is defined as a table, e.g. g = Table[ cos[l1*3.]*sqrt[l2*1.]*l3 + l1*1 , {l1, 0, 3}, {l2, 0, 3}, {l3, 0, 3}]; then, I need to save it in ...
3answers
284 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 ...
0answers
77 views

### Det and MatrixRank freezes on SparseArray with nonzero default value

Why does the following simple code never come to an end (at least with version 8) n = 5; mat = SparseArray[{i_, i_} -> 1, {n, n}, -1/(n - 1)]; MatrixRank[mat] ...
1answer
124 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 ...
1answer
167 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 ...
1answer
74 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 ...
0answers
40 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. ...
1answer
188 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 ...
1answer
242 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 ...
3answers
291 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 ...
0answers
163 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 ...
6answers
628 views