def testMatrixApprox(self):
tol = 10**-6
A = numpy.random.rand(10, 10)
A = A.dot(A.T)
n = 5
inds = numpy.sort(numpy.random.permutation(A.shape[0])[0:n])
AHat = Nystrom.matrixApprox(A, inds)
n = 10
AHat2 = Nystrom.matrixApprox(A, n)
self.assertTrue(numpy.linalg.norm(A - AHat2) < numpy.linalg.norm(A - AHat))
self.assertTrue(numpy.linalg.norm(A - AHat2) < tol)
#Test on a sparse matrix
As = scipy.sparse.csr_matrix(A)
n = 5
inds = numpy.sort(numpy.random.permutation(A.shape[0])[0:n])
AHat = Nystrom.matrixApprox(As, inds)
n = 10
AHat2 = Nystrom.matrixApprox(As, n)
self.assertTrue(SparseUtils.norm(As - AHat2) < SparseUtils.norm(As - AHat))
self.assertTrue(SparseUtils.norm(As - AHat2) < tol)
#Compare dense and sparse solutions
for n in range(1, 9):
inds = numpy.sort(numpy.random.permutation(A.shape[0])[0:n])
AHats = Nystrom.matrixApprox(As, inds)
AHat = Nystrom.matrixApprox(A, inds)
self.assertTrue(numpy.linalg.norm(AHat - numpy.array(AHats.todense())) < tol)
def testNorm(self):
numRows = 10
numCols = 10
for k in range(10):
A = scipy.sparse.rand(numRows, numCols, 0.1, "csr")
norm = SparseUtils.norm(A)
norm2 = 0
for i in range(numRows):
for j in range(numCols):
norm2 += A[i, j]**2
norm2 = numpy.sqrt(norm2)
norm3 = numpy.linalg.norm(numpy.array(A.todense()))
self.assertAlmostEquals(norm, norm2)
self.assertAlmostEquals(norm, norm3)