def rsvd(A, k, p=10, q=2, omega=None):
"""
Compute the randomised SVD using the algorithm on page 9 of Halko et al.,
Finding Structure with randomness: stochastic algorithms for constructing
approximate matrix decompositions, 2009.
Finds the partial SVD of a sparse or dense matrix A, resolving the largest k
singular vectors/values, using exponent q and k+p projections. Returns the
left and right singular vectors, and the singular values. The resulting matrix
can be approximated using A ~ U s V.T. To improve the approximation quality
for a fixed k, increase p or q.
:param A: A sparse or dense matrix or GeneralLinearOperator
:param k: The number of singular values and random projections
:param p: The oversampling parameter
:param q: The exponent for the projections.
:param omega: An initial matrix to perform random projections onto with at least k columns
:return U: The left singular vectors
:return s: The singular values
:return V: The right singular vectors
"""
Parameter.checkInt(k, 1, float("inf"))
Parameter.checkInt(p, 0, float("inf"))
Parameter.checkInt(q, 0, float("inf"))
if isinstance(A, GeneralLinearOperator):
L = A
else:
L = GeneralLinearOperator.asLinearOperator(A)
n = L.shape[1]
if omega is None:
omega = numpy.random.randn(n, k + p)
else:
omega = numpy.c_[omega, numpy.random.randn(n, p + k - omega.shape[1])]
Y = L.matmat(omega)
Q, R = numpy.linalg.qr(Y)
del omega
for i in range(q):
Y = L.rmatmat(Q)
Q, R = numpy.linalg.qr(Y)
gc.collect()
Y = L.matmat(Q)
Q, R = numpy.linalg.qr(Y)
gc.collect()
del Y
del R
gc.collect()
B = L.rmatmat(Q).T
U, s, V = numpy.linalg.svd(B, full_matrices=False)
del B
V = V.T
U = Q.dot(U)
U = U[:, 0:k]
s = s[0:k]
V = V[:, 0:k]
return U, s, V
def rsvd(A, k, p=10, q=2, omega=None):
"""
Compute the randomised SVD using the algorithm on page 9 of Halko et al.,
Finding Structure with randomness: stochastic algorithms for constructing
approximate matrix decompositions, 2009.
Finds the partial SVD of a sparse or dense matrix A, resolving the largest k
singular vectors/values, using exponent q and k+p projections. Returns the
left and right singular vectors, and the singular values. The resulting matrix
can be approximated using A ~ U s V.T. To improve the approximation quality
for a fixed k, increase p or q.
:param A: A sparse or dense matrix or GeneralLinearOperator
:param k: The number of singular values and random projections
:param p: The oversampling parameter
:param q: The exponent for the projections.
:param omega: An initial matrix to perform random projections onto with at least k columns
:return U: The left singular vectors
:return s: The singular values
:return V: The right singular vectors
"""
Parameter.checkInt(k, 1, float("inf"))
Parameter.checkInt(p, 0, float("inf"))
Parameter.checkInt(q, 0, float("inf"))
if isinstance(A, GeneralLinearOperator):
L = A
else:
L = GeneralLinearOperator.asLinearOperator(A)
n = L.shape[1]
if omega is None:
omega = numpy.random.randn(n, k + p)
else:
omega = numpy.c_[omega, numpy.random.randn(n, p + k - omega.shape[1])]
Y = L.matmat(omega)
Q, R = numpy.linalg.qr(Y)
del omega
for i in range(q):
Y = L.rmatmat(Q)
Q, R = numpy.linalg.qr(Y)
gc.collect()
Y = L.matmat(Q)
Q, R = numpy.linalg.qr(Y)
gc.collect()
del Y
del R
gc.collect()
B = L.rmatmat(Q).T
U, s, V = numpy.linalg.svd(B, full_matrices=False)
del B
V = V.T
U = Q.dot(U)
U = U[:, 0:k]
s = s[0:k]
V = V[:, 0:k]
return U, s, V
def testCheckInt(self):
min = 0
max = 5
i = 2
Parameter.checkInt(i, min, max)
Parameter.checkInt(min, min, max)
Parameter.checkInt(max, min, max)
Parameter.checkInt(i, i, i)
self.assertRaises(ValueError, Parameter.checkInt, i, max, min)
self.assertRaises(ValueError, Parameter.checkInt, i, float(min), max)
self.assertRaises(ValueError, Parameter.checkInt, i, min, float(max))
#self.assertRaises(ValueError, Parameter.checkInt, 2.0, min, max)
self.assertRaises(ValueError, Parameter.checkInt, -1, min, max)
self.assertRaises(ValueError, Parameter.checkInt, 6, min, max)
#Check half ranges such as [0, inf]
Parameter.checkInt(i, min, float("inf"))
Parameter.checkInt(i, float("-inf"), max)
#Check use of numpy int32
min = numpy.int32(0)
max = numpy.int32(5)
i = numpy.int32(2)
Parameter.checkInt(i, min, max)
Parameter.checkInt(min, min, max)
Parameter.checkInt(max, min, max)
Parameter.checkInt(i, i, i)
#Test using an array with 1 int
i = numpy.array([1], numpy.int)
logging.debug((type(i)))
self.assertRaises(ValueError, Parameter.checkInt, i, min, max)
