The [Matrix Market](https://math.nist.gov/MatrixMarket/) is> a visual repository of test data for use in comparative studies of algorithms> for numerical linear algebra, featuring nearly 500 sparse matrices> from a variety of applications, as well as matrix generation tools and services
proposed by the National Institute of Standards and Technology (NIST),
a branch of the US Department of Commerce. As the [Matrix Market info page](https://math.nist.gov/MatrixMarket/info.html) puts it,
> The Matrix Market is a component of the NIST project on> [Tools for Evaluation of Mathematical and Statistical Software](https://math.nist.gov/temss/)> which has focus areas in linear algebra, special functions and statistics.
The `.mtx` Matrix Market Exchange format is documented on the
[NIST page on Matrix Market Exchange formats](https://math.nist.gov/MatrixMarket/formats.html).
Having saved the following into a file called `adjacency.mtx`:
%%MatrixMarket matrix coordinate real symmetric
%
% adjacency matrix for a graph
%
5 5 6
1 2 1.000e+00
1 3 1.000e+00
1 5 1.000e+00
2 4 1.000e+00
3 4 1.000e+00
4 5 1.000e+00
one can use input-output functionality in SciPy to read that file
into a SciPy sparse matrix:
sage: from scipy.io import mmread
sage: a = mmread('adjacency.mtx')
which is represented as follows:
sage: a
<5x5 sparse matrix of type ''
with 12 stored elements in COOrdinate format>
and, if one want the list of its entries, prints out as follows:
sage: print(a)
(0, 1) 1.0
(0, 2) 1.0
(0, 4) 1.0
(1, 3) 1.0
(2, 3) 1.0
(3, 4) 1.0
(1, 0) 1.0
(2, 0) 1.0
(4, 0) 1.0
(3, 1) 1.0
(3, 2) 1.0
(4, 3) 1.0
One can convert it to a SciPy dense matrix:
sage: b = a.todense()
sage: b
matrix([[ 0., 1., 1., 0., 1.],
[ 1., 0., 0., 1., 0.],
[ 1., 0., 0., 1., 0.],
[ 0., 1., 1., 0., 1.],
[ 1., 0., 0., 1., 0.]])
and then convert that to a Sage matrix:
sage: c = matrix(b)
sage: c
[0.0 1.0 1.0 0.0 1.0]
[1.0 0.0 0.0 1.0 0.0]
[1.0 0.0 0.0 1.0 0.0]
[0.0 1.0 1.0 0.0 1.0]
[1.0 0.0 0.0 1.0 0.0]
from which one can create a graph:
sage: g = Graph(c)
sage: g
Graph on 5 vertices
sage: g.plot()
Launched png viewer for Graphics object consisting of 12 graphics primitives
Alternatively, to call Octave or MATLAB from SageMath, one can use the
corresponding [interfaces](https://wiki.sagemath.org/Interfaces):
- [SageMath interface to Octave](http://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/octave.html)
- [SageMath interface to MATLAB](http://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/matlab.html)
but for the needs of this question, that should not be necessary.
In summary:
sage: from scipy.io import mmread
sage: g = Graph(matrix(mmread('adjacency.mtx').todense()))
↧