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

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9
votes
0answers
84 views

Efficient solution of huge sparse linear system

I'm trying to improve efficiency of my code in which main task is a solution to huge (~$10^4\times 10^4$) but sparse linear system $$Ax=b$$ (In fact my aim is to solve nonlinear equations $F(x)=0$, ...
6
votes
0answers
183 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 ...
4
votes
0answers
128 views

Finding eigenvalues in Mathematica: why so slow?

I am trying to find the eigensystem of a large sparse real symmetric matrix, and I only need the lowest 40 or so eigenstates. The relevant code is as follows: ...
4
votes
0answers
110 views

How can I force the use of sparse diagonalization methods?

When I evaluate the Eigenvalues function on a very large (e.g. 2^16 x 2^16) sparse matrix, Mathematica says something like: Because finding 65536 out of the ...
3
votes
0answers
91 views

How to speed up summing a large number of vectors

First let me explain what I am trying to do in my code. Assume that I send a very short chirp (2,000 ms long) into a domain filled with 20,000 particles randomly scattered in the domain. The ...
3
votes
0answers
97 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
0answers
100 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) ...
2
votes
0answers
61 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
2
votes
0answers
97 views

Memory used by SparseArray objects

In dealing with a quantum mechanics problem, I am representing some many-body states in two different ways in Mathematica. For two parameters n and ...
0
votes
0answers
35 views

What is stored for a sparse matrix in memory?

I am wondering if a sparse matrix is stored in memory as a list which is its ArrayRules? The reason to ask this is I am trying to write a function to produce a large sparse matrix. However, I am not ...