def merge(self, other, decay=1.0):
"""Merge current :class:`~gensim.models.lsimodel.Projection` instance with another.
Warnings
--------
The content of `other` is destroyed in the process, so pass this function a copy of `other`
if you need it further. The `other` :class:`~gensim.models.lsimodel.Projection` is expected to contain
the same number of features.
Parameters
----------
other : :class:`~gensim.models.lsimodel.Projection`
The Projection object to be merged into the current one. It will be destroyed after merging.
decay : float, optional
Weight of existing observations relatively to new ones.
Setting `decay` < 1.0 causes re-orientation towards new data trends in the input document stream,
by giving less emphasis to old observations. This allows LSA to gradually "forget" old observations
(documents) and give more preference to new ones.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy()
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError(
"vector space mismatch: update is using %s features, expected %s" % (other.m, self.m)
)
logger.info("merging projections: %s + %s", str(self.u.shape), str(other.u.shape))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with ORGQR.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in scipy? And is it fast(er)?
# find component of u2 orthogonal to u1
logger.debug("constructing orthogonal component")
self.u = asfarray(self.u, 'self.u')
c = np.dot(self.u.T, other.u)
self.u = ascarray(self.u, 'self.u')
other.u -= np.dot(self.u, c)
other.u = [other.u] # do some reference magic and call qr_destroy, to save RAM
q, r = matutils.qr_destroy(other.u) # q, r = QR(component)
assert not other.u
# find the rotation that diagonalizes r
k = np.bmat([
[np.diag(decay * self.s), np.multiply(c, other.s)],
[matutils.pad(np.array([]).reshape(0, 0), min(m, n2), n1), np.multiply(r, other.s)]
])
logger.debug("computing SVD of %s dense matrix", k.shape)
try:
# in np < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'.
# for these early versions of np, catch the error and try to compute
# SVD again, but over k*k^T.
# see http://www.mail-archive.com/[email protected]/msg07224.html and
# bug ticket http://projects.scipy.org/np/ticket/706
# sdoering: replaced np's linalg.svd with scipy's linalg.svd:
# TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper
# for partial svd/eigendecomp in np :( //sdoering: maybe there is one in scipy?
u_k, s_k, _ = scipy.linalg.svd(k, full_matrices=False)
except scipy.linalg.LinAlgError:
logger.error("SVD(A) failed; trying SVD(A * A^T)")
# if this fails too, give up with an exception
u_k, s_k, _ = scipy.linalg.svd(np.dot(k, k.T), full_matrices=False)
s_k = np.sqrt(s_k) # go back from eigen values to singular values
k = clip_spectrum(s_k ** 2, self.k)
u1_k, u2_k, s_k = np.array(u_k[:n1, :k]), np.array(u_k[n1:, :k]), s_k[:k]
# update & rotate current basis U = [U, U']*[U1_k, U2_k]
logger.debug("updating orthonormal basis U")
self.s = s_k
self.u = ascarray(self.u, 'self.u')
self.u = np.dot(self.u, u1_k)
q = ascarray(q, 'q')
q = np.dot(q, u2_k)
self.u += q
# make each column of U start with a non-negative number (to force canonical decomposition)
if self.u.shape[0] > 0:
for i in range(self.u.shape[1]):
if self.u[0, i] < 0.0:
self.u[:, i] *= -1.0
def stochastic_svd(corpus, rank, num_terms, chunksize=20000, extra_dims=None,
power_iters=0, dtype=np.float64, eps=1e-6):
"""Run truncated Singular Value Decomposition (SVD) on a sparse input.
Parameters
----------
corpus : {iterable of list of (int, float), scipy.sparse}
Input corpus as a stream (does not have to fit in RAM)
or a sparse matrix of shape (`num_terms`, num_documents).
rank : int
Desired number of factors to be retained after decomposition.
num_terms : int
The number of features (terms) in `corpus`.
chunksize : int, optional
Number of documents to be used in each training chunk.
extra_dims : int, optional
Extra samples to be used besides the rank `k`. Can improve accuracy.
power_iters: int, optional
Number of power iteration steps to be used. Increasing the number of power iterations improves accuracy,
but lowers performance.
dtype : numpy.dtype, optional
Enforces a type for elements of the decomposed matrix.
eps: float, optional
Percentage of the spectrum's energy to be discarded.
Notes
-----
The corpus may be larger than RAM (iterator of vectors), if `corpus` is a `scipy.sparse.csc` instead,
it is assumed the whole corpus fits into core memory and a different (more efficient) code path is chosen.
This may return less than the requested number of top `rank` factors, in case the input itself is of lower rank.
The `extra_dims` (oversampling) and especially `power_iters` (power iterations) parameters affect accuracy of the
decomposition.
This algorithm uses `2 + power_iters` passes over the input data. In case you can only afford a single pass,
set `onepass=True` in :class:`~gensim.models.lsimodel.LsiModel` and avoid using this function directly.
The decomposition algorithm is based on `"Finding structure with randomness:
Probabilistic algorithms for constructing approximate matrix decompositions" <https://arxiv.org/abs/0909.4061>`_.
Returns
-------
(np.ndarray 2D, np.ndarray 1D)
The left singular vectors and the singular values of the `corpus`.
"""
rank = int(rank)
if extra_dims is None:
samples = max(10, 2 * rank) # use more samples than requested factors, to improve accuracy
else:
samples = rank + int(extra_dims)
logger.info("using %i extra samples and %i power iterations", samples - rank, power_iters)
num_terms = int(num_terms)
# first phase: construct the orthonormal action matrix Q = orth(Y) = orth((A * A.T)^q * A * O)
# build Y in blocks of `chunksize` documents (much faster than going one-by-one
# and more memory friendly than processing all documents at once)
y = np.zeros(dtype=dtype, shape=(num_terms, samples))
logger.info("1st phase: constructing %s action matrix", str(y.shape))
if scipy.sparse.issparse(corpus):
m, n = corpus.shape
assert num_terms == m, "mismatch in number of features: %i in sparse matrix vs. %i parameter" % (m, num_terms)
o = np.random.normal(0.0, 1.0, (n, samples)).astype(y.dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(m, n, samples, corpus.indptr, corpus.indices,
corpus.data, o.ravel(), y.ravel()) # y = corpus * o
del o
# unlike np, scipy.sparse `astype()` copies everything, even if there is no change to dtype!
# so check for equal dtype explicitly, to avoid the extra memory footprint if possible
if y.dtype != dtype:
y = y.astype(dtype)
logger.info("orthonormalizing %s action matrix", str(y.shape))
y = [y]
q, _ = matutils.qr_destroy(y) # orthonormalize the range
logger.debug("running %i power iterations", power_iters)
for _ in range(power_iters):
q = corpus.T * q
q = [corpus * q]
q, _ = matutils.qr_destroy(q) # orthonormalize the range after each power iteration step
else:
num_docs = 0
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i', (chunk_no * chunksize))
# construct the chunk as a sparse matrix, to minimize memory overhead
# definitely avoid materializing it as a dense (num_terms x chunksize) matrix!
s = sum(len(doc) for doc in chunk)
chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=dtype) # documents = columns of sparse CSC
m, n = chunk.shape
assert m == num_terms
assert n <= chunksize # the very last chunk of A is allowed to be smaller in size
num_docs += n
logger.debug("multiplying chunk * gauss")
o = np.random.normal(0.0, 1.0, (n, samples)).astype(dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(
m, n, samples, chunk.indptr, chunk.indices, # y = y + chunk * o
chunk.data, o.ravel(), y.ravel()
)
del chunk, o
y = [y]
q, _ = matutils.qr_destroy(y) # orthonormalize the range
for power_iter in range(power_iters):
logger.info("running power iteration #%i", power_iter + 1)
yold = q.copy()
q[:] = 0.0
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i/%i', chunk_no * chunksize, num_docs)
# documents = columns of sparse CSC
chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=dtype)
tmp = chunk.T * yold
tmp = chunk * tmp
del chunk
q += tmp
del yold
q = [q]
q, _ = matutils.qr_destroy(q) # orthonormalize the range
qt = q[:, :samples].T.copy()
del q
if scipy.sparse.issparse(corpus):
b = qt * corpus
logger.info("2nd phase: running dense svd on %s matrix", str(b.shape))
u, s, vt = scipy.linalg.svd(b, full_matrices=False)
del b, vt
else:
# second phase: construct the covariance matrix X = B * B.T, where B = Q.T * A
# again, construct X incrementally, in chunks of `chunksize` documents from the streaming
# input corpus A, to avoid using O(number of documents) memory
x = np.zeros(shape=(qt.shape[0], qt.shape[0]), dtype=dtype)
logger.info("2nd phase: constructing %s covariance matrix", str(x.shape))
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i/%i', chunk_no * chunksize, num_docs)
chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=qt.dtype)
b = qt * chunk # dense * sparse matrix multiply
del chunk
x += np.dot(b, b.T) # TODO should call the BLAS routine SYRK, but there is no SYRK wrapper in scipy :(
del b
# now we're ready to compute decomposition of the small matrix X
logger.info("running dense decomposition on %s covariance matrix", str(x.shape))
# could use linalg.eigh, but who cares... and svd returns the factors already sorted :)
u, s, vt = scipy.linalg.svd(x)
# sqrt to go back from singular values of X to singular values of B = singular values of the corpus
s = np.sqrt(s)
q = qt.T.copy()
del qt
logger.info("computing the final decomposition")
keep = clip_spectrum(s ** 2, rank, discard=eps)
u = u[:, :keep].copy()
s = s[:keep]
u = np.dot(q, u)
return u.astype(dtype), s.astype(dtype)
def merge(self, other, decay=1.0):
"""
Merge this Projection with another.
The content of `other` is destroyed in the process, so pass this function a
copy of `other` if you need it further.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy()
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError("vector space mismatch: update is using %s features, expected %s" %
(other.m, self.m))
logger.info("merging projections: %s + %s" % (str(self.u.shape), str(other.u.shape)))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with ORGQR.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in scipy? And is it fast(er)?
# find component of u2 orthogonal to u1
logger.debug("constructing orthogonal component")
self.u = asfarray(self.u, 'self.u')
c = numpy.dot(self.u.T, other.u)
self.u = ascarray(self.u, 'self.u')
other.u -= numpy.dot(self.u, c)
other.u = [other.u] # do some reference magic and call qr_destroy, to save RAM
q, r = matutils.qr_destroy(other.u) # q, r = QR(component)
assert not other.u
# find the rotation that diagonalizes r
k = numpy.bmat([[numpy.diag(decay * self.s), numpy.multiply(c, other.s)],
[matutils.pad(numpy.array([]).reshape(0, 0), min(m, n2), n1), numpy.multiply(r, other.s)]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
try:
# in numpy < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'.
# for these early versions of numpy, catch the error and try to compute
# SVD again, but over k*k^T.
# see http://www.mail-archive.com/[email protected]/msg07224.html and
# bug ticket http://projects.scipy.org/numpy/ticket/706
# sdoering: replaced numpy's linalg.svd with scipy's linalg.svd:
u_k, s_k, _ = scipy.linalg.svd(k, full_matrices=False) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :( //sdoering: maybe there is one in scipy?
except scipy.linalg.LinAlgError:
logger.error("SVD(A) failed; trying SVD(A * A^T)")
u_k, s_k, _ = scipy.linalg.svd(numpy.dot(k, k.T), full_matrices=False) # if this fails too, give up with an exception
s_k = numpy.sqrt(s_k) # go back from eigen values to singular values
k = clip_spectrum(s_k**2, self.k)
u1_k, u2_k, s_k = numpy.array(u_k[:n1, :k]), numpy.array(u_k[n1:, :k]), s_k[:k]
# update & rotate current basis U = [U, U']*[U1_k, U2_k]
logger.debug("updating orthonormal basis U")
self.s = s_k
self.u = ascarray(self.u, 'self.u')
self.u = numpy.dot(self.u, u1_k)
q = ascarray(q, 'q')
q = numpy.dot(q, u2_k)
self.u += q
# make each column of U start with a non-negative number (to force canonical decomposition)
if self.u.shape[0] > 0:
for i in xrange(self.u.shape[1]):
if self.u[0, i] < 0.0:
self.u[:, i] *= -1.0
def stochastic_svd(corpus, rank, num_terms, chunksize=20000, extra_dims=None,
power_iters=0, dtype=numpy.float64, eps=1e-6):
"""
Run truncated Singular Value Decomposition (SVD) on a sparse input.
Return (U, S): the left singular vectors and the singular values of the input
data stream `corpus` [4]_. The corpus may be larger than RAM (iterator of vectors).
This may return less than the requested number of top `rank` factors, in case
the input itself is of lower rank. The `extra_dims` (oversampling) and especially
`power_iters` (power iterations) parameters affect accuracy of the decomposition.
This algorithm uses `2+power_iters` passes over the input data. In case you can only
afford a single pass, set `onepass=True` in :class:`LsiModel` and avoid using
this function directly.
The decomposition algorithm is based on
**Halko, Martinsson, Tropp. Finding structure with randomness, 2009.**
.. [4] If `corpus` is a scipy.sparse matrix instead, it is assumed the whole
corpus fits into core memory and a different (more efficient) code path is chosen.
"""
rank = int(rank)
if extra_dims is None:
samples = max(10, 2 * rank) # use more samples than requested factors, to improve accuracy
else:
samples = rank + int(extra_dims)
logger.info("using %i extra samples and %i power iterations" % (samples - rank, power_iters))
num_terms = int(num_terms)
# first phase: construct the orthonormal action matrix Q = orth(Y) = orth((A * A.T)^q * A * O)
# build Y in blocks of `chunksize` documents (much faster than going one-by-one
# and more memory friendly than processing all documents at once)
y = numpy.zeros(dtype=dtype, shape=(num_terms, samples))
logger.info("1st phase: constructing %s action matrix" % str(y.shape))
if scipy.sparse.issparse(corpus):
m, n = corpus.shape
assert num_terms == m, "mismatch in number of features: %i in sparse matrix vs. %i parameter" % (m, num_terms)
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(y.dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(m, n, samples, corpus.indptr, corpus.indices,
corpus.data, o.ravel(), y.ravel()) # y = corpus * o
del o
# unlike numpy, scipy.sparse `astype()` copies everything, even if there is no change to dtype!
# so check for equal dtype explicitly, to avoid the extra memory footprint if possible
if y.dtype != dtype:
y = y.astype(dtype)
logger.info("orthonormalizing %s action matrix" % str(y.shape))
y = [y]
q, _ = matutils.qr_destroy(y) # orthonormalize the range
logger.debug("running %i power iterations" % power_iters)
for power_iter in xrange(power_iters):
q = corpus.T * q
q = [corpus * q]
q, _ = matutils.qr_destroy(q) # orthonormalize the range after each power iteration step
else:
num_docs = 0
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i' % (chunk_no * chunksize))
# construct the chunk as a sparse matrix, to minimize memory overhead
# definitely avoid materializing it as a dense (num_terms x chunksize) matrix!
s = sum(len(doc) for doc in chunk)
chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=dtype) # documents = columns of sparse CSC
m, n = chunk.shape
assert m == num_terms
assert n <= chunksize # the very last chunk of A is allowed to be smaller in size
num_docs += n
logger.debug("multiplying chunk * gauss")
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(m, n, samples, chunk.indptr, chunk.indices, # y = y + chunk * o
chunk.data, o.ravel(), y.ravel())
del chunk, o
y = [y]
q, _ = matutils.qr_destroy(y) # orthonormalize the range
for power_iter in xrange(power_iters):
logger.info("running power iteration #%i" % (power_iter + 1))
yold = q.copy()
q[:] = 0.0
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i/%i' % (chunk_no * chunksize, num_docs))
chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=dtype) # documents = columns of sparse CSC
tmp = chunk.T * yold
tmp = chunk * tmp
del chunk
q += tmp
del yold
q = [q]
q, _ = matutils.qr_destroy(q) # orthonormalize the range
qt = q[:, :samples].T.copy()
del q
if scipy.sparse.issparse(corpus):
b = qt * corpus
logger.info("2nd phase: running dense svd on %s matrix" % str(b.shape))
u, s, vt = scipy.linalg.svd(b, full_matrices=False)
del b, vt
else:
# second phase: construct the covariance matrix X = B * B.T, where B = Q.T * A
# again, construct X incrementally, in chunks of `chunksize` documents from the streaming
# input corpus A, to avoid using O(number of documents) memory
x = numpy.zeros(shape=(qt.shape[0], qt.shape[0]), dtype=numpy.float64)
logger.info("2nd phase: constructing %s covariance matrix" % str(x.shape))
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i/%i' % (chunk_no * chunksize, num_docs))
chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=qt.dtype)
b = qt * chunk # dense * sparse matrix multiply
del chunk
x += numpy.dot(b, b.T) # TODO should call the BLAS routine SYRK, but there is no SYRK wrapper in scipy :(
del b
# now we're ready to compute decomposition of the small matrix X
logger.info("running dense decomposition on %s covariance matrix" % str(x.shape))
u, s, vt = scipy.linalg.svd(x) # could use linalg.eigh, but who cares... and svd returns the factors already sorted :)
s = numpy.sqrt(s) # sqrt to go back from singular values of X to singular values of B = singular values of the corpus
q = qt.T.copy()
del qt
logger.info("computing the final decomposition")
keep = clip_spectrum(s**2, rank, discard=eps)
u = u[:, :keep].copy()
s = s[:keep]
u = numpy.dot(q, u)
return u.astype(dtype), s.astype(dtype)
def merge(self, other, decay=1.0):
"""
Merge this Projection with another.
The content of `other` is destroyed in the process, so pass this function a
copy of `other` if you need it further.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy()
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError(
"vector space mismatch: update is using %s features, expected %s"
% (other.m, self.m))
logger.info("merging projections: %s + %s" %
(str(self.u.shape), str(other.u.shape)))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with ORGQR.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in scipy? And is it fast(er)?
# find component of u2 orthogonal to u1
logger.debug("constructing orthogonal component")
self.u = asfarray(self.u, 'self.u')
c = numpy.dot(self.u.T, other.u)
self.u = ascarray(self.u, 'self.u')
other.u -= numpy.dot(self.u, c)
other.u = [
other.u
] # do some reference magic and call qr_destroy, to save RAM
q, r = matutils.qr_destroy(other.u) # q, r = QR(component)
assert not other.u
# find the rotation that diagonalizes r
k = numpy.bmat(
[[numpy.diag(decay * self.s),
numpy.multiply(c, other.s)],
[
matutils.pad(numpy.array([]).reshape(0, 0), min(m, n2), n1),
numpy.multiply(r, other.s)
]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
try:
# in numpy < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'.
# for these early versions of numpy, catch the error and try to compute
# SVD again, but over k*k^T.
# see http://www.mail-archive.com/[email protected]/msg07224.html and
# bug ticket http://projects.scipy.org/numpy/ticket/706
# sdoering: replaced numpy's linalg.svd with scipy's linalg.svd:
u_k, s_k, _ = scipy.linalg.svd(
k, full_matrices=False
) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :( //sdoering: maybe there is one in scipy?
except scipy.linalg.LinAlgError:
logger.error("SVD(A) failed; trying SVD(A * A^T)")
u_k, s_k, _ = scipy.linalg.svd(
numpy.dot(k, k.T), full_matrices=False
) # if this fails too, give up with an exception
s_k = numpy.sqrt(
s_k) # go back from eigen values to singular values
k = clip_spectrum(s_k**2, self.k)
u1_k, u2_k, s_k = numpy.array(u_k[:n1, :k]), numpy.array(
u_k[n1:, :k]), s_k[:k]
# update & rotate current basis U = [U, U']*[U1_k, U2_k]
logger.debug("updating orthonormal basis U")
self.s = s_k
self.u = ascarray(self.u, 'self.u')
self.u = numpy.dot(self.u, u1_k)
q = ascarray(q, 'q')
q = numpy.dot(q, u2_k)
self.u += q
# make each column of U start with a non-negative number (to force canonical decomposition)
if self.u.shape[0] > 0:
for i in xrange(self.u.shape[1]):
if self.u[0, i] < 0.0:
self.u[:, i] *= -1.0
def merge(self, other, decay=1.0):
"""Merge current :class:`~gensim.models.lsimodel.Projection` instance with another.
Warnings
--------
The content of `other` is destroyed in the process, so pass this function a copy of `other`
if you need it further. The `other` :class:`~gensim.models.lsimodel.Projection` is expected to contain
the same number of features.
Parameters
----------
other : :class:`~gensim.models.lsimodel.Projection`
The Projection object to be merged into the current one. It will be destroyed after merging.
decay : float, optional
Weight of existing observations relatively to new ones.
Setting `decay` < 1.0 causes re-orientation towards new data trends in the input document stream,
by giving less emphasis to old observations. This allows LSA to gradually "forget" old observations
(documents) and give more preference to new ones.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy()
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError(
"vector space mismatch: update is using %s features, expected %s" % (other.m, self.m)
)
logger.info("merging projections: %s + %s", str(self.u.shape), str(other.u.shape))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with ORGQR.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in scipy? And is it fast(er)?
# find component of u2 orthogonal to u1
logger.debug("constructing orthogonal component")
self.u = asfarray(self.u, 'self.u')
c = np.dot(self.u.T, other.u)
self.u = ascarray(self.u, 'self.u')
other.u -= np.dot(self.u, c)
other.u = [other.u] # do some reference magic and call qr_destroy, to save RAM
q, r = matutils.qr_destroy(other.u) # q, r = QR(component)
assert not other.u
# find the rotation that diagonalizes r
k = np.bmat([
[np.diag(decay * self.s), np.multiply(c, other.s)],
[matutils.pad(np.array([]).reshape(0, 0), min(m, n2), n1), np.multiply(r, other.s)]
])
logger.debug("computing SVD of %s dense matrix", k.shape)
try:
# in np < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'.
# for these early versions of np, catch the error and try to compute
# SVD again, but over k*k^T.
# see http://www.mail-archive.com/[email protected]/msg07224.html and
# bug ticket http://projects.scipy.org/np/ticket/706
# sdoering: replaced np's linalg.svd with scipy's linalg.svd:
# TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper
# for partial svd/eigendecomp in np :( //sdoering: maybe there is one in scipy?
u_k, s_k, _ = scipy.linalg.svd(k, full_matrices=False)
except scipy.linalg.LinAlgError:
logger.error("SVD(A) failed; trying SVD(A * A^T)")
# if this fails too, give up with an exception
u_k, s_k, _ = scipy.linalg.svd(np.dot(k, k.T), full_matrices=False)
s_k = np.sqrt(s_k) # go back from eigen values to singular values
k = clip_spectrum(s_k ** 2, self.k)
u1_k, u2_k, s_k = np.array(u_k[:n1, :k]), np.array(u_k[n1:, :k]), s_k[:k]
# update & rotate current basis U = [U, U']*[U1_k, U2_k]
logger.debug("updating orthonormal basis U")
self.s = s_k
self.u = ascarray(self.u, 'self.u')
self.u = np.dot(self.u, u1_k)
q = ascarray(q, 'q')
q = np.dot(q, u2_k)
self.u += q
# make each column of U start with a non-negative number (to force canonical decomposition)
if self.u.shape[0] > 0:
for i in range(self.u.shape[1]):
if self.u[0, i] < 0.0:
self.u[:, i] *= -1.0
def stochasticSvd(corpus,
rank,
num_terms,
chunks=20000,
extra_dims=None,
power_iters=0,
dtype=numpy.float64,
eps=1e-6):
"""
Return (U, S): the left singular vectors and the singular values of the streamed
input corpus `corpus` [3]_.
This may actually return less than the requested number of top `rank` factors,
in case the input is of lower rank. The `extra_dims` (oversampling) and especially
`power_iters` (power iterations) parameters affect accuracy of the decomposition.
This algorithm uses `2+power_iters` passes over the data. In case you can only
afford a single pass over the input corpus, set `onepass=True` in :class:`LsiModel`
and avoid using this algorithm directly.
The decomposition algorithm is based on
**Halko, Martinsson, Tropp. Finding structure with randomness, 2009.**
.. [3] If `corpus` is a scipy.sparse matrix instead, it is assumed the whole
corpus fits into core memory and a different (more efficient) code path is chosen.
"""
rank = int(rank)
if extra_dims is None:
samples = max(
10, 2 * rank
) # use more samples than requested factors, to improve accuracy
else:
samples = rank + int(extra_dims)
logger.info("using %i extra samples and %i power iterations" %
(samples - rank, power_iters))
num_terms = int(num_terms)
eps = max(
float(eps), 1e-9
) # must ignore near-zero eigenvalues (probably numerical error); the associated eigenvectors are typically unstable/garbage
# first phase: construct the orthonormal action matrix Q = orth(Y) = orth((A * A.T)^q * A * O)
# build Y in blocks of `chunks` documents (much faster than going one-by-one
# and more memory friendly than processing all documents at once)
y = numpy.zeros(dtype=dtype, shape=(num_terms, samples))
logger.info("1st phase: constructing %s action matrix" % str(y.shape))
if scipy.sparse.issparse(corpus):
m, n = corpus.shape
assert num_terms == m, "mismatch in number of features: %i in sparse matrix vs. %i parameter" % (
m, num_terms)
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(
y.dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(m, n, samples, corpus.indptr,
corpus.indices, corpus.data, o.ravel(),
y.ravel()) # y = corpus * o
del o
y = y.astype(
dtype
) # TODO unlike numpy, scipy actually makes a copy even when dtype=y.dtype...marginally inefficient
logger.debug("running %i power iterations" % power_iters)
for power_iter in xrange(power_iters):
y = corpus.T * y
y = corpus * y
else:
chunker = itertools.groupby(enumerate(corpus),
key=lambda (docno, doc): docno / chunks)
num_docs = 0
for chunk_no, (key, group) in enumerate(chunker):
logger.info('PROGRESS: at document #%i' % (chunk_no * chunks))
# construct the chunk as a sparse matrix, to minimize memory overhead
# definitely avoid materializing it as a dense (num_terms x chunks) matrix!
chunk = matutils.corpus2csc(
(doc for _, doc in group), num_terms=num_terms,
dtype=dtype) # documents = columns of sparse CSC
m, n = chunk.shape
assert m == num_terms
assert n <= chunks # the very last chunk of A is allowed to be smaller in size
num_docs += n
logger.debug("multiplying chunk * gauss")
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(
dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(
num_terms,
n,
samples,
chunk.indptr, # y = y + chunk * o
chunk.indices,
chunk.data,
o.ravel(),
y.ravel())
del chunk, o
for power_iter in xrange(power_iters):
logger.info("running power iteration #%i" % (power_iter + 1))
yold = y.copy()
y[:] = 0.0
chunker = itertools.groupby(enumerate(corpus),
key=lambda
(docno, doc): docno / chunks)
for chunk_no, (key, group) in enumerate(chunker):
logger.info('PROGRESS: at document #%i/%i' %
(chunk_no * chunks, num_docs))
chunk = matutils.corpus2csc(
(doc for _, doc in group),
num_terms=num_terms,
dtype=dtype) # documents = columns of sparse CSC
tmp = chunk.T * yold
tmp = chunk * tmp
del chunk
y += tmp
del yold
logger.info("orthonormalizing %s action matrix" % str(y.shape))
y = [y]
q, r = matutils.qr_destroy(y) # orthonormalize the range
del y
samples = clipSpectrum(numpy.diag(r), samples, discard=eps)
qt = numpy.asfortranarray(
q[:, :samples].T
) # discard bogus columns, in case Y was rank-deficient
del q
if scipy.sparse.issparse(corpus):
b = qt * corpus
logger.info("2nd phase: running dense svd on %s matrix" % str(b.shape))
u, s, vt = numpy.linalg.svd(b, full_matrices=False)
del b, vt
else:
# second phase: construct the covariance matrix X = B * B.T, where B = Q.T * A
# again, construct X incrementally, in chunks of `chunks` documents from the streaming
# input corpus A, to avoid using O(number of documents) memory
x = numpy.zeros(shape=(samples, samples), dtype=dtype)
logger.info("2nd phase: constructing %s covariance matrix" %
str(x.shape))
chunker = itertools.groupby(enumerate(corpus),
key=lambda (docno, doc): docno / chunks)
for chunk_no, (key, group) in enumerate(chunker):
logger.info('PROGRESS: at document #%i/%i' %
(chunk_no * chunks, num_docs))
chunk = matutils.corpus2csc((doc for _, doc in group),
num_terms=num_terms,
dtype=dtype)
b = qt * chunk # dense * sparse matrix multiply
x += numpy.dot(
b, b.T
) # TODO should call the BLAS routine SYRK, but there is no SYRK wrapper in scipy :(
del chunk, b
# now we're ready to compute decomposition of the small matrix X
logger.info("running dense decomposition on %s covariance matrix" %
str(x.shape))
u, s, vt = numpy.linalg.svd(
x
) # could use linalg.eigh, but who cares... and svd returns the factors already sorted :)
s = numpy.sqrt(
s
) # sqrt to go back from singular values of X to singular values of B = singular values of the corpus
logger.info("computing the final decomposition")
keep = clipSpectrum(s**2, rank, discard=eps)
u = numpy.asfortranarray(u[:, :keep])
s = s[:keep]
gemm = matutils.blas('gemm', u)
u = gemm(1.0, qt, u, trans_a=True)
return u, s
def merge(self, other, decay=1.0):
"""
Merge this Projection with another.
The content of `other` is destroyed in the process, so pass this function a
copy of `other` if you need it further.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy('F')
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError(
"vector space mismatch: update is using %s features, expected %s"
% (other.m, self.m))
logger.info("merging projections: %s + %s" %
(str(self.u.shape), str(other.u.shape)))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with ORGQR.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in scipy? And is it fast(er)?
# find component of u2 orthogonal to u1
# IMPORTANT: keep matrices in memory suitable order for matrix products; failing to do so gives 8x lower performance :(
self.u = numpy.asfortranarray(
self.u) # does nothing if input already fortran-order array
other.u = numpy.asfortranarray(other.u)
gemm = matutils.blas('gemm', self.u)
logger.debug("constructing orthogonal component")
c = gemm(1.0, self.u, other.u, trans_a=True)
gemm(-1.0, self.u, c, beta=1.0, c=other.u, overwrite_c=True)
other.u = [
other.u
] # do some reference magic and call qr_destroy, to save RAM
q, r = matutils.qr_destroy(other.u) # q, r = QR(component)
assert not other.u
# find the rotation that diagonalizes r
k = numpy.bmat([[numpy.diag(decay * self.s), c * other.s],
[
matutils.pad(
numpy.matrix([]).reshape(0, 0), min(m, n2),
n1), r * other.s
]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
try:
# in numpy < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'.
# for these early versions of numpy, catch the error and try to compute
# SVD again, but over k*k^T.
# see http://www.mail-archive.com/[email protected]/msg07224.html and
# bug ticket http://projects.scipy.org/numpy/ticket/706
u_k, s_k, _ = numpy.linalg.svd(
k, full_matrices=False
) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :(
except numpy.linalg.LinAlgError:
logging.error("SVD(A) failed; trying SVD(A * A^T)")
u_k, s_k, _ = numpy.linalg.svd(
numpy.dot(k, k.T), full_matrices=False
) # if this fails too, give up with an exception
s_k = numpy.sqrt(
s_k) # go back from eigen values to singular values
k = clipSpectrum(s_k**2, self.k)
u1_k, u2_k, s_k = u_k[:n1, :k].copy('F'), u_k[n1:, :k].copy(
'F'), s_k[:k]
# update & rotate current basis U = [U, U']*[U1_k, U2_k]
logger.debug("updating orthonormal basis U")
self.u = gemm(
1.0, self.u, u1_k
) # TODO temporarily creates an extra (m,k) dense array in memory. find a way to avoid this!
gemm(1.0, q, u2_k, beta=1.0, c=self.u, overwrite_c=True)
self.s = s_k
def stochasticSvd(corpus, rank, num_terms, chunks=20000, extra_dims=None,
power_iters=0, dtype=numpy.float64, eps=1e-6):
"""
Return (U, S): the left singular vectors and the singular values of the streamed
input corpus `corpus` [3]_.
This may actually return less than the requested number of top `rank` factors,
in case the input is of lower rank. The `extra_dims` (oversampling) and especially
`power_iters` (power iterations) parameters affect accuracy of the decomposition.
This algorithm uses `2+power_iters` passes over the data. In case you can only
afford a single pass over the input corpus, set `onepass=True` in :class:`LsiModel`
and avoid using this algorithm directly.
The decomposition algorithm is based on
**Halko, Martinsson, Tropp. Finding structure with randomness, 2009.**
.. [3] If `corpus` is a scipy.sparse matrix instead, it is assumed the whole
corpus fits into core memory and a different (more efficient) code path is chosen.
"""
rank = int(rank)
if extra_dims is None:
samples = max(10, 2 * rank) # use more samples than requested factors, to improve accuracy
else:
samples = rank + int(extra_dims)
logger.info("using %i extra samples and %i power iterations" % (samples - rank, power_iters))
num_terms = int(num_terms)
eps = max(float(eps), 1e-9) # must ignore near-zero eigenvalues (probably numerical error); the associated eigenvectors are typically unstable/garbage
# first phase: construct the orthonormal action matrix Q = orth(Y) = orth((A * A.T)^q * A * O)
# build Y in blocks of `chunks` documents (much faster than going one-by-one
# and more memory friendly than processing all documents at once)
y = numpy.zeros(dtype = dtype, shape = (num_terms, samples))
logger.info("1st phase: constructing %s action matrix" % str(y.shape))
if scipy.sparse.issparse(corpus):
m, n = corpus.shape
assert num_terms == m, "mismatch in number of features: %i in sparse matrix vs. %i parameter" % (m, num_terms)
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(y.dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(m, n, samples, corpus.indptr, corpus.indices,
corpus.data, o.ravel(), y.ravel()) # y = corpus * o
del o
y = y.astype(dtype) # TODO unlike numpy, scipy actually makes a copy even when dtype=y.dtype...marginally inefficient
logger.debug("running %i power iterations" % power_iters)
for power_iter in xrange(power_iters):
y = corpus.T * y
y = corpus * y
else:
chunker = itertools.groupby(enumerate(corpus), key = lambda (docno, doc): docno / chunks)
num_docs = 0
for chunk_no, (key, group) in enumerate(chunker):
logger.info('PROGRESS: at document #%i' % (chunk_no * chunks))
# construct the chunk as a sparse matrix, to minimize memory overhead
# definitely avoid materializing it as a dense (num_terms x chunks) matrix!
chunk = matutils.corpus2csc((doc for _, doc in group), num_terms=num_terms, dtype=dtype) # documents = columns of sparse CSC
m, n = chunk.shape
assert m == num_terms
assert n <= chunks # the very last chunk of A is allowed to be smaller in size
num_docs += n
logger.debug("multiplying chunk * gauss")
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(num_terms, n, samples, chunk.indptr, # y = y + chunk * o
chunk.indices, chunk.data, o.ravel(), y.ravel())
del chunk, o
for power_iter in xrange(power_iters):
logger.info("running power iteration #%i" % (power_iter + 1))
yold = y.copy()
y[:] = 0.0
chunker = itertools.groupby(enumerate(corpus), key = lambda (docno, doc): docno / chunks)
for chunk_no, (key, group) in enumerate(chunker):
logger.info('PROGRESS: at document #%i/%i' % (chunk_no * chunks, num_docs))
chunk = matutils.corpus2csc((doc for _, doc in group), num_terms=num_terms, dtype=dtype) # documents = columns of sparse CSC
tmp = chunk.T * yold
tmp = chunk * tmp
del chunk
y += tmp
del yold
logger.info("orthonormalizing %s action matrix" % str(y.shape))
y = [y]
q, r = matutils.qr_destroy(y) # orthonormalize the range
del y
samples = clipSpectrum(numpy.diag(r), samples, discard = eps)
qt = numpy.asfortranarray(q[:, :samples].T) # discard bogus columns, in case Y was rank-deficient
del q
if scipy.sparse.issparse(corpus):
b = qt * corpus
logger.info("2nd phase: running dense svd on %s matrix" % str(b.shape))
u, s, vt = numpy.linalg.svd(b, full_matrices=False)
del b, vt
else:
# second phase: construct the covariance matrix X = B * B.T, where B = Q.T * A
# again, construct X incrementally, in chunks of `chunks` documents from the streaming
# input corpus A, to avoid using O(number of documents) memory
x = numpy.zeros(shape = (samples, samples), dtype = dtype)
logger.info("2nd phase: constructing %s covariance matrix" % str(x.shape))
chunker = itertools.groupby(enumerate(corpus), key = lambda (docno, doc): docno / chunks)
for chunk_no, (key, group) in enumerate(chunker):
logger.info('PROGRESS: at document #%i/%i' % (chunk_no * chunks, num_docs))
chunk = matutils.corpus2csc((doc for _, doc in group), num_terms=num_terms, dtype=dtype)
b = qt * chunk # dense * sparse matrix multiply
x += numpy.dot(b, b.T) # TODO should call the BLAS routine SYRK, but there is no SYRK wrapper in scipy :(
del chunk, b
# now we're ready to compute decomposition of the small matrix X
logger.info("running dense decomposition on %s covariance matrix" % str(x.shape))
u, s, vt = numpy.linalg.svd(x) # could use linalg.eigh, but who cares... and svd returns the factors already sorted :)
s = numpy.sqrt(s) # sqrt to go back from singular values of X to singular values of B = singular values of the corpus
logger.info("computing the final decomposition")
keep = clipSpectrum(s**2, rank, discard=eps)
u = numpy.asfortranarray(u[:, :keep])
s = s[:keep]
gemm = matutils.blas('gemm', u)
u = gemm(1.0, qt, u, trans_a=True)
return u, s
def merge(self, other, decay=1.0):
"""
Merge this Projection with another.
The content of `other` is destroyed in the process, so pass this function a
copy of `other` if you need it further.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy('F')
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError("vector space mismatch: update is using %s features, expected %s" %
(other.m, self.m))
logger.info("merging projections: %s + %s" % (str(self.u.shape), str(other.u.shape)))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with ORGQR.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in scipy? And is it fast(er)?
# find component of u2 orthogonal to u1
# IMPORTANT: keep matrices in memory suitable order for matrix products; failing to do so gives 8x lower performance :(
self.u = numpy.asfortranarray(self.u) # does nothing if input already fortran-order array
other.u = numpy.asfortranarray(other.u)
gemm = matutils.blas('gemm', self.u)
logger.debug("constructing orthogonal component")
c = gemm(1.0, self.u, other.u, trans_a = True)
gemm(-1.0, self.u, c, beta = 1.0, c = other.u, overwrite_c = True)
other.u = [other.u] # do some reference magic and call qr_destroy, to save RAM
q, r = matutils.qr_destroy(other.u) # q, r = QR(component)
assert not other.u
# find the rotation that diagonalizes r
k = numpy.bmat([[numpy.diag(decay * self.s), c * other.s], [matutils.pad(numpy.matrix([]).reshape(0, 0), min(m, n2), n1), r * other.s]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
try:
# in numpy < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'.
# for these early versions of numpy, catch the error and try to compute
# SVD again, but over k*k^T.
# see http://www.mail-archive.com/[email protected]/msg07224.html and
# bug ticket http://projects.scipy.org/numpy/ticket/706
u_k, s_k, _ = numpy.linalg.svd(k, full_matrices = False) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :(
except numpy.linalg.LinAlgError:
logging.error("SVD(A) failed; trying SVD(A * A^T)")
u_k, s_k, _ = numpy.linalg.svd(numpy.dot(k, k.T), full_matrices = False) # if this fails too, give up with an exception
s_k = numpy.sqrt(s_k) # go back from eigen values to singular values
k = clipSpectrum(s_k ** 2, self.k)
u1_k, u2_k, s_k = u_k[:n1, :k].copy('F'), u_k[n1:, :k].copy('F'), s_k[:k]
# update & rotate current basis U = [U, U']*[U1_k, U2_k]
logger.debug("updating orthonormal basis U")
self.u = gemm(1.0, self.u, u1_k) # TODO temporarily creates an extra (m,k) dense array in memory. find a way to avoid this!
gemm(1.0, q, u2_k, beta = 1.0, c = self.u, overwrite_c = True)
self.s = s_k
def stochastic_svd(corpus,
rank,
num_terms,
chunksize=20000,
extra_dims=None,
power_iters=0,
dtype=numpy.float64,
eps=1e-6):
"""
Return (U, S): the left singular vectors and the singular values of the streamed
input corpus `corpus` [3]_.
This may actually return less than the requested number of top `rank` factors,
in case the input is of lower rank. The `extra_dims` (oversampling) and especially
`power_iters` (power iterations) parameters affect accuracy of the decomposition.
This algorithm uses `2+power_iters` passes over the data. In case you can only
afford a single pass over the input corpus, set `onepass=True` in :class:`LsiModel`
and avoid using this algorithm directly.
The decomposition algorithm is based on
**Halko, Martinsson, Tropp. Finding structure with randomness, 2009.**
.. [3] If `corpus` is a scipy.sparse matrix instead, it is assumed the whole
corpus fits into core memory and a different (more efficient) code path is chosen.
"""
rank = int(rank)
if extra_dims is None:
samples = max(
10, 2 * rank
) # use more samples than requested factors, to improve accuracy
else:
samples = rank + int(extra_dims)
logger.info("using %i extra samples and %i power iterations" %
(samples - rank, power_iters))
num_terms = int(num_terms)
# first phase: construct the orthonormal action matrix Q = orth(Y) = orth((A * A.T)^q * A * O)
# build Y in blocks of `chunksize` documents (much faster than going one-by-one
# and more memory friendly than processing all documents at once)
y = numpy.zeros(dtype=dtype, shape=(num_terms, samples))
logger.info("1st phase: constructing %s action matrix" % str(y.shape))
if scipy.sparse.issparse(corpus):
m, n = corpus.shape
assert num_terms == m, "mismatch in number of features: %i in sparse matrix vs. %i parameter" % (
m, num_terms)
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(
y.dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(m, n, samples, corpus.indptr,
corpus.indices, corpus.data, o.ravel(),
y.ravel()) # y = corpus * o
del o
# unlike numpy, scipy.sparse `astype()` copies everything, even if there is no change to dtype!
# so check for equal dtype explicitly, to avoid the extra memory footprint if possible
if y.dtype != dtype:
y = y.astype(dtype)
logger.info("orthonormalizing %s action matrix" % str(y.shape))
y = [y]
q, _ = matutils.qr_destroy(y) # orthonormalize the range
logger.debug("running %i power iterations" % power_iters)
for power_iter in xrange(power_iters):
q = corpus.T * q
q = [corpus * q]
q, _ = matutils.qr_destroy(
q) # orthonormalize the range after each power iteration step
else:
num_docs = 0
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i' % (chunk_no * chunksize))
# construct the chunk as a sparse matrix, to minimize memory overhead
# definitely avoid materializing it as a dense (num_terms x chunksize) matrix!
s = sum(len(doc) for doc in chunk)
chunk = matutils.corpus2csc(
chunk, num_terms=num_terms,
dtype=dtype) # documents = columns of sparse CSC
m, n = chunk.shape
assert m == num_terms
assert n <= chunksize # the very last chunk of A is allowed to be smaller in size
num_docs += n
logger.debug("multiplying chunk * gauss")
o = numpy.random.normal(0.0, 1.0, (n, samples)).astype(
dtype) # draw a random gaussian matrix
sparsetools.csc_matvecs(
m,
n,
samples,
chunk.indptr,
chunk.indices, # y = y + chunk * o
chunk.data,
o.ravel(),
y.ravel())
del chunk, o
y = [y]
q, _ = matutils.qr_destroy(y) # orthonormalize the range
for power_iter in xrange(power_iters):
logger.info("running power iteration #%i" % (power_iter + 1))
yold = q.copy()
q[:] = 0.0
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i/%i' %
(chunk_no * chunksize, num_docs))
chunk = matutils.corpus2csc(
chunk, num_terms=num_terms,
dtype=dtype) # documents = columns of sparse CSC
tmp = chunk.T * yold
tmp = chunk * tmp
del chunk
q += tmp
del yold
q = [q]
q, _ = matutils.qr_destroy(q) # orthonormalize the range
qt = q[:, :samples].T.copy()
del q
if scipy.sparse.issparse(corpus):
b = qt * corpus
logger.info("2nd phase: running dense svd on %s matrix" % str(b.shape))
u, s, vt = numpy.linalg.svd(b, full_matrices=False)
del b, vt
else:
# second phase: construct the covariance matrix X = B * B.T, where B = Q.T * A
# again, construct X incrementally, in chunks of `chunksize` documents from the streaming
# input corpus A, to avoid using O(number of documents) memory
x = numpy.zeros(shape=(qt.shape[0], qt.shape[0]), dtype=numpy.float64)
logger.info("2nd phase: constructing %s covariance matrix" %
str(x.shape))
for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)):
logger.info('PROGRESS: at document #%i/%i' %
(chunk_no * chunksize, num_docs))
chunk = matutils.corpus2csc(chunk,
num_terms=num_terms,
dtype=qt.dtype)
b = qt * chunk # dense * sparse matrix multiply
del chunk
x += numpy.dot(
b, b.T
) # TODO should call the BLAS routine SYRK, but there is no SYRK wrapper in scipy :(
del b
# now we're ready to compute decomposition of the small matrix X
logger.info("running dense decomposition on %s covariance matrix" %
str(x.shape))
u, s, vt = numpy.linalg.svd(
x
) # could use linalg.eigh, but who cares... and svd returns the factors already sorted :)
s = numpy.sqrt(
s
) # sqrt to go back from singular values of X to singular values of B = singular values of the corpus
q = qt.T.copy()
del qt
logger.info("computing the final decomposition")
keep = clip_spectrum(s**2, rank, discard=eps)
u = u[:, :keep].copy()
s = s[:keep]
u = numpy.dot(q, u)
return u.astype(dtype), s.astype(dtype)
