def testAsLinearOperator(self):
try:
import scipy.sparse.linalg
#Check it works for the eigenvalue solver
L = GeneralLinearOperator.asLinearOperator(self.A)
k = 10
s, V = scipy.sparse.linalg.eigsh(L, k, which="LA")
inds = numpy.flipud(numpy.argsort(s))
s = s[inds]
V = V[:, inds]
B = self.A.toarray()
s2, V2 = numpy.linalg.eigh(B)
inds = numpy.flipud(numpy.argsort(s2))[0:k]
s2 = s2[inds]
V2 = V2[:, inds]
nptst.assert_array_almost_equal(s, s2[0:s.shape[0]])
nptst.assert_array_almost_equal((V * s).dot(V.T),
(V2 * s2).dot(V2.T))
except:
print("Couldn't test asLinearOperator")
def time_ns():
density = 10**-3
ns = var_range * 10**4
times = numpy.zeros((5, ns.shape[0]))
for i, n in enumerate(ns):
# Generate random sparse matrix
inds = numpy.random.randint(n, size=(2, n * n * density))
data = numpy.random.rand(n * n * density)
A = scipy.sparse.csc_matrix((data, inds), (n, n))
A_sppy = sppy.csarray(A, storagetype="row")
L = GeneralLinearOperator.asLinearOperator(A_sppy, parallel=True)
print(A.shape, A.nnz)
times[0, i] = time_reps(svds, (A, k), reps)
times[1, i] = time_reps(svdp, (A, k), reps)
# times[2, i] = time_reps(sparsesvd, (A, k), reps)
times[3, i] = time_reps(truncated_svd.fit, (A,), reps)
times[4, i] = time_reps(sppy.linalg.rsvd, (L, k, p, n_iter), reps)
print(n, density, times[:, i])
plt.figure(1)
plt.plot(ns, times[0, :], 'k-', label="ARPACK")
plt.plot(ns, times[1, :], 'r-', label="PROPACK")
# plt.plot(ns, times[2, :], 'b-', label="SparseSVD")
plt.plot(ns, times[3, :], 'k--', label="sklearn RSVD")
plt.plot(ns, times[4, :], 'r--', label="sppy RSVD")
plt.legend(loc="upper left")
plt.xlabel("n")
plt.ylabel("time (s)")
plt.savefig("time_ns.png", format="png")
def time_ns():
density = 10**-3
ns = var_range * 10**4
times = numpy.zeros((5, ns.shape[0]))
for i, n in enumerate(ns):
# Generate random sparse matrix
inds = numpy.random.randint(n, size=(2, n * n * density))
data = numpy.random.rand(n * n * density)
A = scipy.sparse.csc_matrix((data, inds), (n, n))
A_sppy = sppy.csarray(A, storagetype="row")
L = GeneralLinearOperator.asLinearOperator(A_sppy, parallel=True)
print(A.shape, A.nnz)
times[0, i] = time_reps(svds, (A, k), reps)
times[1, i] = time_reps(svdp, (A, k), reps)
# times[2, i] = time_reps(sparsesvd, (A, k), reps)
times[3, i] = time_reps(truncated_svd.fit, (A, ), reps)
times[4, i] = time_reps(sppy.linalg.rsvd, (L, k, p, n_iter), reps)
print(n, density, times[:, i])
plt.figure(1)
plt.plot(ns, times[0, :], 'k-', label="ARPACK")
plt.plot(ns, times[1, :], 'r-', label="PROPACK")
# plt.plot(ns, times[2, :], 'b-', label="SparseSVD")
plt.plot(ns, times[3, :], 'k--', label="sklearn RSVD")
plt.plot(ns, times[4, :], 'r--', label="sppy RSVD")
plt.legend(loc="upper left")
plt.xlabel("n")
plt.ylabel("time (s)")
plt.savefig("time_ns.png", format="png")
def testAsLinearOperatorSum(self):
n = 10
m = 5
density = 0.3
A = rand((n, m), density)
B = rand((n, m), density)
L = GeneralLinearOperator.asLinearOperator(A)
M = GeneralLinearOperator.asLinearOperator(B)
N = GeneralLinearOperator.asLinearOperatorSum(L, M)
k = 3
V = numpy.random.rand(m, k)
W = numpy.random.rand(n, k)
U = N.matmat(V)
U2 = A.dot(V) + B.dot(V)
nptst.assert_array_almost_equal(U, U2)
U = N.rmatmat(W)
U2 = A.T.dot(W) + B.T.dot(W)
nptst.assert_array_almost_equal(U, U2)
v = numpy.random.rand(m)
w = numpy.random.rand(n)
u = N.matvec(v)
u2 = A.dot(v) + B.dot(v)
nptst.assert_array_almost_equal(u, u2)
u = N.rmatvec(w)
u2 = A.T.dot(w) + B.T.dot(w)
nptst.assert_array_almost_equal(u, u2)
#See if we get an error if A, B are different shapes
B = rand((m, n), 0.1)
M = GeneralLinearOperator.asLinearOperator(B)
self.assertRaises(ValueError,
GeneralLinearOperator.asLinearOperatorSum, L, M)
def testAsLinearOperatorSum(self):
n = 10
m = 5
density = 0.3
A = rand((n, m), density)
B = rand((n, m), density)
L = GeneralLinearOperator.asLinearOperator(A)
M = GeneralLinearOperator.asLinearOperator(B)
N = GeneralLinearOperator.asLinearOperatorSum(L, M)
k = 3
V = numpy.random.rand(m, k)
W = numpy.random.rand(n, k)
U = N.matmat(V)
U2 = A.dot(V) + B.dot(V)
nptst.assert_array_almost_equal(U, U2)
U = N.rmatmat(W)
U2 = A.T.dot(W) + B.T.dot(W)
nptst.assert_array_almost_equal(U, U2)
v = numpy.random.rand(m)
w = numpy.random.rand(n)
u = N.matvec(v)
u2 = A.dot(v) + B.dot(v)
nptst.assert_array_almost_equal(u, u2)
u = N.rmatvec(w)
u2 = A.T.dot(w) + B.T.dot(w)
nptst.assert_array_almost_equal(u, u2)
#See if we get an error if A, B are different shapes
B = rand((m, n), 0.1)
M = GeneralLinearOperator.asLinearOperator(B)
self.assertRaises(ValueError, GeneralLinearOperator.asLinearOperatorSum, L, M)
def profilePowerIteration2(self):
p = 100
q = 5
omega = numpy.random.randn(self.X.shape[1], p)
L = GeneralLinearOperator.asLinearOperator(self.X, parallel=True)
def run():
Y = L.matmat(omega)
for i in range(q):
Y = L.rmatmat(Y)
Y = L.matmat(Y)
ProfileUtils.profile('run()', globals(), locals())
def testAsLinearOperator(self):
try:
import scipy.sparse.linalg
#Check it works for the eigenvalue solver
L = GeneralLinearOperator.asLinearOperator(self.A)
k = 10
s, V = scipy.sparse.linalg.eigsh(L, k, which="LA")
inds = numpy.flipud(numpy.argsort(s))
s = s[inds]
V = V[:, inds]
B = self.A.toarray()
s2, V2 = numpy.linalg.eigh(B)
inds = numpy.flipud(numpy.argsort(s2))[0:k]
s2 = s2[inds]
V2 = V2[:, inds]
nptst.assert_array_almost_equal(s, s2[0:s.shape[0]])
nptst.assert_array_almost_equal((V*s).dot(V.T), (V2*s2).dot(V2.T))
except:
print("Couldn't test asLinearOperator")