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

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1answer
74 views

What would be the Mathematica equivalent of sparse in MATLAB?

The sparse function in MATLAB does the following: S = sparse(i,j,v) generates a sparse matrix S from the triplets i, j, and v such that S(i(k),j(k)) = v(k). The ...
9
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1answer
142 views

Something wrong when I apply Derivative on a SparseArray

Bug introduced in v5.0 or earlier, and persisting through v10.4.1. There, I create a SparseArray using command ...
0
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0answers
36 views

Matrix with equations as entries - how to choose them and solve them

I have a matrix in Mathematica, which I have built using Normal[SparseArray]. Each entry of this matrix is an equation in one variable. What I need to do is 1) to select some of the entries of the ...
10
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2answers
115 views

Using Cases to pick out entries of a SparseArray

I'm trying to use a SparseArray for some large homological algebra calculations. I'd like to find indices of a SparseArray ...
10
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0answers
112 views

Possible Bug in LinearSolveFunction with Sparse Vectors

Bug introduced in 5.0 and persists through 10.4.1 LinearSolveFunction is new in 5.0 Consider the following set of equations and corresponding variables: ...
0
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0answers
67 views

How to compile code that involve sparse array?

I have the following code ...
7
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3answers
159 views

Nonzero element positions of a matrix

Let m={{1, 2, 0}, {4, 0, 9}}; I want to find the position of every nonzero element of the above matrix. The code ...
4
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1answer
62 views

How to create overlapped block matrices and simplify the result

This is sort of a duplicate of Creating overlapped block matrices, but the question wasn't fully answered since the OP never returned to clarify. I am using Kuba's answer for FEM, but I have been ...
1
vote
3answers
74 views

How to convert a matrix into a sparse matrix [duplicate]

If I have a matrix: row 1)1 0 0 4 row 2)0 0 0 0 row 3)5 1 0 0 row 4)0 5 0 0 row 5)0 0 0 9 How would I put it in a sparse matrix format: ...
1
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1answer
89 views

efficient element wise multiplication of SparseArray vector and matrix

I have a large SparseArray $P$ of dimensions $\{d,d\}$ and I want to multiply a vector (also a SparseArray) $v$ of length $d$ ...
9
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4answers
248 views

How to convert a sparse matrix to a list of sparse arrays?

I have a matrix stored as a SparseArray. How can I convert it to a List of its rows, where each row is stored as a ...
4
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4answers
287 views

Constructing a large tridiagonal matrix with alternating signs

What is the best way to construct a large tridiagonal matrix, in the following form (notably with alternating signs)? $\mathbf M = \begin{pmatrix} 0 & a & 0 & 0 & 0 & \cdots ...
4
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0answers
170 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: ...
0
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1answer
57 views

LinearSolve on non-square matrices?

I just came across a strange behaviour for LinearSolve (on Mathematica 8.0.0.0). Consider the following definitions: ...
5
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4answers
154 views

Add to matrix missing elements (for list of time series)

This question is an extension of the 43122. I’ve looked through many interesting post (like this) but (as always) missed the direct matching. So the setting is simple: ...
1
vote
1answer
55 views

Assemble rule replacement from pairs of positions

I want to create a rule replacement list, which I then use to create a SparseArray. The input is a list of positions of the from ...
4
votes
3answers
164 views

Problem with Conditionals: Why does mathematica add an extra empty list to my output

I have a set of positions where I want to slice a list of numbers. If I Total the values in that list, and they are greater than or equal to 1, I want to remember ...
0
votes
1answer
53 views

Timing and memory use is critical:fast partitioning of binary sparse array

I do experiments were I measure a signal, and I need to know at what time points it is above a threshold. If at a given time point, the signal is above the threshold, then a '1' gets put into the ...
0
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0answers
42 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 ...
2
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0answers
110 views

How to solve lowest eigenvalue with Lanczos or Arnoldi algorithm? [closed]

By setting Method->Arnoldi in Eigensystem I was able to solve lowest eigenvalue and eigenstate of a large sparse matrix. ...
10
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0answers
111 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 $F(x)=0$, ...
18
votes
2answers
207 views

Speeding up generation of block diagonal matrix

I'm struggling with the following problem. I have $48$ square matrices (full, filled with real machine precision numbers, thus are packed, all different) of size $128$. I wolud like to place them on a ...
18
votes
1answer
478 views

Sparse Cholesky Decomposition

I am working with square matrices with a special form, which for large rank ($> 100,000$) would be best stored and manipulated as a SparseArray. I believe that ...
1
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0answers
28 views

Why variable in SparseArray can't be replaced? [duplicate]

SparseArray[{1, 1} -> t] /. t -> 1 Still contains t. Why t is not replaced by 1?
6
votes
1answer
115 views

Adding two SparseArrays produces zeros in the reported “NonzeroValues”

When two SparseArrays are added together and new zero values are created, these new zero values are reported as "NonzeroValues". Example, produced with Mathematica version 10.2: ...
9
votes
2answers
170 views

Does LinearSolve know that I gave it a Sparse lower triangular matrix?

Let $\mathbf L$ be a nonsingular numeric (non-symbolic) large, lower triangular sparse matrix. Let $\mathbf b$ be an appropriately sized vector. I want to solve $\mathbf L\mathbf x=\mathbf b$. ...
19
votes
1answer
210 views

What are pattern sparse arrays and how do I use them?

I found a few references to something called a "pattern sparse array" that does not contain any values, only positions. What is this data structure? How and when do I use it? From the ...
5
votes
3answers
184 views

How to populate a large sparse array efficiently

I am trying to populate a large 2D sparse array and sum up all the columns at the end. I tried generating a set of rules and then generate a matrix using SparseArray or break the data into chunks but ...
3
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0answers
96 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 ...
2
votes
3answers
108 views

How to store the nonzero elements of a sparse array in a file? [duplicate]

Often I need to use same matrix several times and for that I save them in an external file. Converting the matrix into SparseArray can save a lot of space in this ...
4
votes
3answers
382 views

Constructing Tri-Diagonal Matrices

Fractional Calculus Course, we are instructed to create an $n \times n$ Tri-Diagonal matrix in the form of: \begin{array} a A &= \begin{bmatrix} 2 & -1 & 0 & 0 & ... ...
2
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1answer
136 views

When are sparse arrays effective?

Sparse arrays are not effective in Mathematica 10. More computational time is needed to perform arithmetic operations on sparse arrays. Their size is also bigger than normal arrays. Here is a simple ...
10
votes
2answers
243 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
2
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0answers
71 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 ...
4
votes
0answers
138 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 ...
2
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1answer
66 views

Non-numeric elements in banded sparse array

The documentation mentions that "the elements in SparseArray need not be numeric", although "the individual elements of a sparse array cannot themselves be lists." ...
17
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1answer
307 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 and fixed in 10.3.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 ...
2
votes
4answers
174 views

Given a matrix of integer, create a matrix with 1 or 0 according to which numbers are in the first matrix

Not sure the title gives the idea of what I need, so here is a sample: I have ten (w) combinations (subsets) of 20 (n) numbers taken 4 (k) at time. I need a matrix of dimension w x n with 0/1 in each ...
2
votes
1answer
175 views

Memory usage optimization for a large Association/SparseArray

Reformulating my question in simpler terms. Take two lists list1 = RandomInteger[{1, 100000000}, 25000000]; list2 = RandomReal[{1, 10}, 25000000]; Make an ...
28
votes
1answer
583 views

What are SparseArray Properties? How and when should they be used?

A strange undocumented form of SparseArray is increasingly used in answers on this site: ...
10
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0answers
241 views

LinearSolve and Krylov Method options

I need to solve a large, sparse, linear system. At some point Method -> "Multifrontal" fails and a bit later also "Pardiso" ...
2
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0answers
112 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 ...
1
vote
2answers
74 views

conditional rules for sparse matrix

why does the following not work (Table isn't plugging in values for k): ...
-1
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1answer
110 views

Laplace equation

I tried to run this code, but it doesn't work for NDSolve ...
-2
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1answer
120 views

Recreating in Mathematica a matrix created in Python [closed]

I need to recreate in Mathematica this matrix that I created in Python: ...
1
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2answers
110 views

Filing matrix by bands [closed]

I need to fill a matrix, CSI, by taking elements from an array, inverse, which is the Inverse Fast Fourier Transform of an array ...
2
votes
1answer
91 views

sparse array with list [closed]

i'm trying to populate a sparse array with lists in certain positions, i tried the following code, ...
3
votes
1answer
121 views

speeding up creation of SparseArray

I have to create the following sparse arrays, which are reshaped in a two dimensional matrix, so that i can use the build in Dot[] function to do a kind of ...
5
votes
4answers
532 views

Elegant mehod of generating this matrix?

Good evening, I need to determine an elegant (as possible) method of computing an nxn matrix below (the matrix shown is just a 16x16 example). I've been toying with For loops, Tables, Bands, ...