In [3]:
import numpy as np
import scipy.sparse as sparse
import scipy.linalg as sla
import scipy.sparse.linalg as spla
import matplotlib.pyplot as plt
%matplotlib inline


Let's make a random sparse matrix

First we'll set the density so that $$density = \frac{nnz(A)}{n^2}$$

In [4]:
n = 100
density = 10.0 / n # 5 points per row
nnz = int(n*n*density)


Now make the entries:

In [5]:
def randsp(n, density):
nnz = int(n*n*density)
row = np.random.random_integers(low=0, high=n-1, size=nnz)
col = np.random.random_integers(low=0, high=n-1, size=nnz)
data = np.ones(nnz, dtype=float)

A = sparse.coo_matrix((data, (row, col)), shape=(n, n))
return A


But let's make it positive definite:

In [7]:
A = randsp(100, 5/100.)
plt.spy(A, marker='.')

Out[7]:
<matplotlib.lines.Line2D at 0x111658940>
In [8]:
A = randsp(100, 2/100.)
plt.spy(A, marker='.')

Out[8]:
<matplotlib.lines.Line2D at 0x1117004a8>
In [9]:
A = randsp(100, 50/100.)
plt.spy(A, marker='.')

Out[9]:
<matplotlib.lines.Line2D at 0x11171f8d0>
In [10]:
A = randsp(100, 25/100.)
plt.spy(A, marker='.')

Out[10]:
<matplotlib.lines.Line2D at 0x11183e518>
In [ ]: