Questions on the construction and manipulation of sparse arrays in Mathematica, with functions like SparseArray[] and Band[].
6
votes
1answer
91 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. ...
1
vote
1answer
45 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:
...
2
votes
2answers
89 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 ...
0
votes
1answer
45 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 ...
2
votes
1answer
226 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 ...
3
votes
1answer
114 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:
...
2
votes
1answer
121 views
How to handle a sparse array of lists
I have data in the form of a sparse array of lists. For example:
...
5
votes
0answers
96 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 ...
11
votes
2answers
192 views
Bug with SparseArray selector in Pick
I have created a notebook with two cells. This is the content of the first:
...
4
votes
2answers
107 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 ...
1
vote
2answers
101 views
6
votes
1answer
322 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
votes
3answers
303 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 ...
0
votes
0answers
59 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 ...
0
votes
0answers
45 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 ...
9
votes
1answer
154 views
Sporadic bugs in multidimensional SparseArray objects
Resolution
WRI affirms that SparseArray[__] is broken (in 9.0 and 9.01)
WRI's suggested workaround is SparseArray//Normal
My ...
2
votes
1answer
96 views
Product of non-zero elements in sparse array
How can I multiply the non-zero elements of a SparseArray?
Example:
...
1
vote
1answer
73 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:
...
3
votes
0answers
62 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, ...
2
votes
1answer
93 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
134 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 ...
6
votes
2answers
142 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
95 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
151 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 $1$, ...
-3
votes
1answer
105 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 ...
4
votes
3answers
222 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 ...
2
votes
0answers
74 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]
...
3
votes
1answer
114 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
137 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
70 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
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.
...
2
votes
1answer
168 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
192 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 ...
1
vote
3answers
235 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
156 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 ...
14
votes
6answers
554 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
140 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
289 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
293 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
177 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
465 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
216 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 ...
14
votes
1answer
274 views
Adding three integer sparse matrices is very slow. Adding only two is fast
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 generate a large sparse matrix:
...
5
votes
2answers
240 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 ...
10
votes
1answer
1k views
How to work around Mathematica hanging when showing a large SparseArray?
Note: This is 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
175 views
10
votes
1answer
500 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:
...
8
votes
2answers
342 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 ...
9
votes
2answers
410 views
Speeding up construction of simple tridiagonal matrix
I have the following code to construct a tridiagonal matrix:
...
3
votes
1answer
180 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 ...
